You sure can! Though it does require a different cooking method though. To cook pork shoulder in the oven, put the seasoned pork in a large Dutch oven, fat side up, and roast, uncovered, until lightly browned, 45 minutes. Pour the Dr Pepper over the pork, lower the oven temperature to 300 degrees F, and cover the pot. Cook until the pork is completely tender and pulls easily from the bone.