In a large, heavy pot over medium heat, warm the peanut oil. Add the chicken pieces and brown on all sides, about 5 to 10 minutes. Using a slotted spoon, transfer the chicken to a large plate. Add the stew meat to the pot and brown it on all sides. Remove to the plate with the chicken. Add the bell pepper, onions, scallions, garlic, carrots, and tomatoes to the same pot and sauté over medium heat until they begin to soften, about 10 minutes.
Return the chicken and beef to the pot and add the allspice, thyme, salt, peppers, and 3 cups of the stock (or as much as is needed to cover). Bring to a boil, cover, and reduce the heat to low. Cook for 45 minutes.
Meanwhile, cut the cabbage into 8 wedges and place on a steamer rack over boiling water. Cover and stream until almost tender, about 10 minutes. Remove from the steamer and set aside.
After the meats have cooked for 45 minutes, stir in the rice.