Rinse the chicken pieces under cold running water and pat dry with paper towels. Season with salt, pepper, cumin, and a squeeze of lime juice. Place 4 tablespoons of the oil in a large, heavy-bottomed Dutch oven or sauté pan over medium heat. When the oil is hot, add the chicken pieces and cook, turning occasionally, until golden brown on all sides, 10 to 12 minutes. Reduce the heat to medium-low, cover and cook gently until the chicken is tender and cooked through, 10 to 20 minutes. Remove the chicken to a platter and set it aside until cool enough to handle.
Add 2 to 3 tablespoons of the remaining oil to the pan. Stir in the onion, bell peppers, and garlic. Cook over low to medium-low heat, stirring often, until the vegetables have softened and the onion is translucent, 10 to 12 minutes. Add the tomatoes and cook, stirring occasionally, for another 15 to 20 minutes. Remove 1 cup of the tomato mixture and set it aside. Stir the sherry, olives, and capers into the remaining tomato mixture. Taste and season with cumin. Cover with the lid slightly askew. Simmer the sauce over low heat until slightly thickened, 10 to 15 minutes. Set aside.
Remove and discard the skin and bones from the chicken. Cut the meat into bite-sized pieces and add it to the tomato sauce. Taste and adjust the seasonings if necessary. Set aside.
Preheat the oven to 350°F. Oil an 8-by-12-by-2½-inch baking dish.
In a food processor with a steel knife blade, or in a blender, puree the corn. In a large, heavy-bottomed saucepan, combine the puree with the cream, sugar, and the reserved 1 cup tomato sauce. Taste and adjust the seasonings. Cook the corn mixture, uncovered, over medium heat, stirring often, until the mixture thickens to the consistency of oatmeal. Remove from the heat, then whisk in the egg yolks one at a time.
Spoon the chicken into the baking dish and cover it with the corn mixture. Bake for 30 minutes. Sprinkle the top with the cheese, then return the tambor to the oven and bake until the top is nicely browned, 10 to 15 minutes. Serve the tambor directly from the baking dish.