In the bowl of a 6-8 quart crockpot pot, add the chicken, onion, garlic, chili powder, oregano, paprika, thyme, allspice, crushed red pepper flakes, bay leaf, salt and pepper.
Next add the tomato paste, chicken broth and balsamic vinegar. Give everything a gentle stir to combine. Cover the crockpot and cook on low for 6 to 8 hours (or 4-6 hours on high) stirring once or twice if possible.
During the last 30 minutes of cooking, stir the broccoli rabe, roasted red peppers and cannellini beans together in a bowl and add to the crockpot. Crank the heat up to high, cover and let cook 20-30 minutes longer. Lightly shred the chicken with two forks, it should just fall apart. Stir in the parmesan and parsley. Ladle the soup into bowls and serve with parmesan and crusty bread for dipping.