An apparatus for cooking and smoking food comprising: a vertically extending cooking and smoking chamber having a left side wall, a right side wall, a back wall, a front opening, and a bottom floor; a door positionable on the front opening for closing and opening the front opening; one or more air intake vents (24, 28) provided in a lower portion of the cooking and smoking chamber; one or more exhaust vents (34, 36) provided in an upper portion of the cooking and smoking chamber; and one or more electric heating elements positioned in the lower portion of the cooking and smoking chamber, the one or more electric heating elements being spaced above the bottom floor of the cooking and smoking chamber; a smoke box (18, 150) for generating smoke; and a smoke box placement station in the cooking and smoking chamber for placement of the smoke box (18, 150) at least partially over the one or more electric heating elements; wherein the smoke box (18, 150) comprises: an interior combustion area for combusting wood chips or other pieces in an oxygen deficient environment to produce smoke and an exhaust flow assembly which defines a circuitous exhaust flow path for the smoke wherein the smoke must flow in a first direction through an inner flow gap formed by the exhaust flow assembly and then must flow in a second direction, different from the first direction, through an outer flow gap formed by the exhaust flow assembly; a first obstructing structure in the inner flow gap; a second obstructing structure in the outer flow gap; wherein the first and the second obstructing structures each comprise an upstream rail (110a, 112a) and a parallel downstream rail (110b, 112b), the upstream and the downstream rails (110a, 112a; 110b, 112b) each have a plurality of holes (114, 116, 118, 120) for flow of the smoke through the rails (110a, 112a; 110b, 112b), and the holes (118, 120) of the downstream rail (110b, 112b) are not in alignment with the holes (114, 116) of the upstream rail (110a, 112a). a vertically extending cooking and smoking chamber having a left side wall, a right side wall, a back wall, a front opening, and a bottom floor; a door positionable on the front opening for closing and opening the front opening; one or more air intake vents (24, 28) provided in a lower portion of the cooking and smoking chamber; one or more exhaust vents (34, 36) provided in an upper portion of the cooking and smoking chamber; and one or more electric heating elements positioned in the lower portion of the cooking and smoking chamber, the one or more electric heating elements being spaced above the bottom floor of the cooking and smoking chamber; a smoke box (18, 150) for generating smoke; and a smoke box placement station in the cooking and smoking chamber for placement of the smoke box (18, 150) at least partially over the one or more electric heating elements; an interior combustion area for combusting wood chips or other pieces in an oxygen deficient environment to produce smoke and an exhaust flow assembly which defines a circuitous exhaust flow path for the smoke wherein the smoke must flow in a first direction through an inner flow gap formed by the exhaust flow assembly and then must flow in a second direction, different from the first direction, through an outer flow gap formed by the exhaust flow assembly; a first obstructing structure in the inner flow gap; a second obstructing structure in the outer flow gap; wherein the first and the second obstructing structures each comprise an upstream rail (110a, 112a) and a parallel downstream rail (110b, 112b), the upstream and the downstream rails (110a, 112a; 110b, 112b) each have a plurality of holes (114, 116, 118, 120) for flow of the smoke through the rails (110a, 112a; 110b, 112b), and the holes (118, 120) of the downstream rail (110b, 112b) are not in alignment with the holes (114, 116) of the upstream rail (110a, 112a).