In a large stock pot, place chicken pieces 1 carrot, 1 rib of celery, and 1 onion (coarsely chop the vegetables), cover with water and bring to a boil on high heat. Once the water is boiling, reduce to a simmer and cook for 45 minutes to 1 hour, until chicken is done. Skim the foam off occasionally.
While cooking the chicken, chop the carrots, onions celery and tomatillos to bite sized pieces, and set aside. Cut the jalapenos in half, lengthwise, and remove the seeds, and the cut into thin strips.
Drain the hominy and beans, and rinse in a colander with cold water.
Chop the cilantro until medium to fine sized pieces.
Remove the chicken from the stock pot, and set aside to cool. Remove the the spent vegetables. Remove the stock from heat.
In a large frying pan, heat the olive oil, and add the onions and garlic. Sauté for about 5 minutes and add the rest of the fresh vegetable, and cook for about 10 minutes, until vegetables are starting to brown.
Pour contents of the frying pan into the stock pot, and add the drained beans and hominy, and the can of tomatoes. Also stir in the cilantro, salt, pepper, cumin, and chili powder.
Bring the soup to a boil on high heat, once boiling, lower to a simmer. Cook until vegetables are tender.
While the soup is cooking, pull the chicken meat of the bones and shred into bite sized pieces.
Mix the masa with 3 tbsp of cold water and mix until a smooth paste is formed. Pour mixture into the soup and bring the soup back to a boil (must thicken at a boil for 4-5 minutes).
Add reserved chicken back to pot. Dice avocados and add to soup, and remove the pot from the heat.
Garnish with fresh chopped cilantro, and Colby-Jack cheese.