In a medium sized bowl, stir together the paprika, ground mustard, cayenne, cloves, pepper, and 1/2 tsp. salt. Add in the cubed chicken and toss to coat. Let the chicken marinate in this seasoning in the fridge, covered for 45 minutes-1 hour.
Cut the sausage into 1/4 inch thick slices and thinly slices enough onions to measure 4 cups. Finely chop the carrot and the bell pepper if you have not done so yet. Then seed the chiles and chop. Drain, seed, and chop the tomatoes.
In a heavy soup kettle heat 1 Tbsp. EVOO over moderately high heat until hot and add in the sausage. Cook until it has browned on each side, and then remove and place on a paper plate lined with a paper towel. Using the same kettle add the chicken that has been marinating and brown chicken on each side - about 6 minutes total. Then transfer the chicken to a plate as well.
Next cook the carrots and 2 cups of the sliced onions, covered, over moderate heat, stirring occasionally and scraping up any brown bits, until carrots and onion have softened. Add the bell pepper, chiles, and garlic and cook, stirring for about 2 minutes. Add in the tomatoes, broth, and hominy with the liquid and bring this mixture to a boil. Add the sausage and chicken in and simmer the stew, covered, for 45 minutes.
Optional but recommended: While the stew is cooking - heat the remaining 2 Tbsp. EVOO in a skillet and place the remaining 2 cups sliced onion in the skillet with 1/4 tsp. salt. Cover and stir occasionally for 15 minutes with the lid on, and 15 minutes uncovered. The onions should be crisp and golden brown - perfect topping for the soup!
Cut the beans into 2 inch pieces. Add them into the stew and cook for 10 minutes, or until beans become tender. Garnish the stew with the crispy onions.