*If you prefer, you may add the broccoli rabe in the beginning of the cooking, but just know it will be cooked down a bit more. It’s still delicious this way, it just has a little less firmness to it.
In the bowl of a 6-8 quart Crock-Pot, add the chicken, onion, garlic, chili powder, oregano, paprika, thyme, allspice, crushed red pepper flakes, bay leaf, salt, and pepper. Add the tomato paste, chicken broth, and balsamic vinegar. Give everything a gentle stir to combine. Cover the Crock-Pot and cook on low for 6-8 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 and add to the Crock-Pot. 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 Parmigiano-Reggiano and parsley.
Ladle the soup into bowls and serve with Parmigiano-Reggiano and crusty bread for dipping.