Inclusion Criteria:  Patients must fulfil all the following criteria:  Female patient is at least 18 years of age, Patient has signed the Informed Consent (ICF) and is able to comply with protocol requirements. Patient with histologically proven endometrial adenocarcinoma with recurrent or advanced disease. Patient with an Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1.  Patient must have primary Stage IIIC2 or Stage IV disease or first recurrent endometrial cancer (see International Federation of Gynecology and Obstetrics staging FIGO Staging 18.1) without curative treatment by radiation therapy or surgery alone or in combination, and meet at least one of the following situations:  Patient has primary Stage IIIC2 (with nodes involvement from the outset, not allowing a curative radiotherapy, or with remaining measurable lumbo-aortic nodes after lumbo-aortic dissection, which cannot be treated by curative radiotherapy) or Stage IV disease. Patient has first recurrent disease and is chemotherapy naïve for this 1st recurrence or metastatic setting. Patient may have received prior neo-adjuvant/adjuvant systemic chemotherapy or loco-regional concomitant radio-chemotherapy for the primary cancer and had a recurrence ≥ 6 months after completing treatment (first recurrence only). All histologic subtypes of endometrial adenocarcinoma could be included if MMRd/MSI-H, Patient with MMRd/MSI-H (defined in routine local IHC), mandatory for inclusion. In case of ambiguous result of IHC (lack of positive internal control, heterogeneous loss of MMR protein expression), the MMRd/MSI-H status will be assessed by PCR/NGS. Availability of 1 block for MMR/MSI status centralized confirmation for IHC or NGS/PCR, and additional block(s) for Translational Research Patient with measurable disease according RECIST 1.1 criteria Patient could have been previously treated with hormone therapy, for the metastatic/advanced disease Patient may have received external beam +/- vaginal brachytherapy  Patient has adequate organ function, defined as follows:  Absolute neutrophil count ≥ 1,500 cells/μL Platelets ≥ 100,000 cells/μL Hemoglobin ≥ 9 g/dL or ≥ 5.6 mmol/L Serum creatinine ≤ 1.5× upper limit of normal (ULN) or calculated creatinine clearance ≥ 50 mL/min using the Cockcroft-Gault equation for patients with creatinine levels > 1.5× institutional ULN Total bilirubin ≤ 1.5× ULN (≤ 2.0 x ULN in patients with known Gilbert's syndrome) or direct bilirubin ≤ 1× ULN Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5× ULN unless liver metastases are present, in which case they must be ≤ 5× ULN International normalized ratio or prothrombin time (PT) ≤1.5× ULN and activated partial thromboplastin time ≤1.5× ULN. Patients receiving anticoagulant therapy must have a PT or partial thromboplastin within the therapeutic range of intended use of anticoagulants.  Patient must have a negative serum pregnancy test within 72 hours of the first dose of study medication, unless they are of nonchildbearing potential. Nonchildbearing potential is defined as follows:  Patient is ≥ 45 years of age and has not had menses for > 1 year. A follicle-stimulating hormone value in the postmenopausal range upon screening evaluation if amenorrhoeic for < 2 years without a hysterectomy and oophorectomy. Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation: Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound, MRI, or CT scan. Tubal ligation must be confirmed with medical records of the actual procedure; otherwise, the patient must fulfil the criteria in Inclusion Criterion 14. Information must be captured appropriately within the site's source documents. 14. Patient of childbearing potential must agree to use a highly effective method of contraception (section 18.9) with their partners starting from time of consent through 150 days after the last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient (Information must be captured appropriately within the site's source documents).  Exclusion Criteria:  Patients are to be excluded from the study if they meet any of the following criteria:  Patient has received neoadjuvant/adjuvant systemic chemotherapy for primary Stage IIIc2 or IV disease and has had a recurrence or PD within 6 months of completing chemotherapy treatment prior to entering the study.  Note: Low-dose cisplatin given as a radiation sensitizer or hormonal therapies do not exclude patients from study participation.  Patient has had > 1 recurrence of endometrial cancer, treated with chemotherapy. Surgery of the recurrence is allowed. Patient previously treated with chemotherapy for non-curable advanced disease or metastatic disease Patient has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent.  Patient has received prior anticancer therapy (chemotherapy, targeted therapies, hormonal therapy, radiotherapy) within 21 days or < 5 times the half-life of the most recent therapy prior to Study Day 1, whichever is shorter.  Note: Palliative radiation therapy to a small field ≥ 1 week prior to Day 1 of study treatment may be allowed.  Patient with contraindication to chemotherapy or checkpoint inhibitor treatments Patient has a concomitant malignancy, or patient has a prior non-endometrial invasive malignancy who has been disease-free for < 3 years or who received any active treatment in the last 3 years for that malignancy. Non-melanoma skin cancer is allowed. Patient has known uncontrolled central nervous system metastases, carcinomatosis meningitis, or both. Note: Patients with previously treated brain metastases may participate provided they are stable (without evidence of disease progression by imaging [using the identical imaging modality for each assessment, either MRI or CT scan] for at least4 weeks prior to the first dose of study treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and have not been using steroids for at least 7 days prior to study treatment. Carcinomatous meningitis precludes a patient from study participation regardless of clinical stability. Patient has a known history of human immunodeficiency virus (HIV; HIV ½ antibodies). Patient has known active hepatitis B (eg, hepatitis B surface antigen reactive) or hepatitis C (eg, hepatitis C virus ribonucleic acid [qualitative] is detected). Patient has an active autoimmune disease that has required systemic treatment in the past 2 years. Replacement therapy is not considered a form of systemic therapy (eg, thyroid hormone or insulin). Patient has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of systemic immunosuppressive therapy within 7 days prior to the first dose of study treatment.  Patient has not recovered (ie, to Grade ≤ 1 or to baseline) from cytotoxic therapy-induced adverse events (AEs).  Note: Patients with Grade ≤ 2 neuropathy, Grade ≤ 2 alopecia, or Grade ≤ 2 fatigue are an exception to this criterion and may qualify for the study.  Patient has not recovered adequately from AEs or complications from any major surgery prior to starting therapy. Patient has a known hypersensitivity to carboplatin, paclitaxel, or dostarlimab components or excipients. Patient is currently participating and receiving study treatment or has participated in a study of an investigational agent and received study treatment or used an investigational device within 4 weeks of the first dose of treatment. Patient is considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease, or active infection requiring systemic therapy. Specific examples include, but are not limited to, active, non-infectious pneumonitis; uncontrolled ventricular arrhythmia; recent (within 90 days) myocardial infarction; uncontrolled major seizure disorder; unstable spinal cord compression; superior vena cava syndrome; or any psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study (including obtaining informed consent).  Use of any of the following immunomodulatory agents within 30 days prior to the first dose of study drug:  Systemic corticosteroids (at dose higher than 10 mg/day equivalent prednisone); if systemic corticoid use at higher dose, corticoid must be stopped at least 7 days before study treatment start Interferons Interleukins Live vaccine Note: Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, BCG, and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed as other killed vaccines, if done at least 2 weeks prior the first dose of study drug; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. Patient is pregnant or breastfeeding or is expecting to conceive children within the projected duration of the study, starting with the screening visit through 180 days after the last dose of study treatment, or lactating woman.