1. Preheat oven to broil. Place peppers on a foil-lined pan and broil until blackened, about 7 minutes. Wrap up in foil to steam, cool. Remove seeds and stems and some of charred skins (we like to keep some on). Rough chop and set aside.
2. Place hominy and BBQ pork and chicken stock in saucepan. Heat 10 minutes. Add peppers and tomatoes and more chicken stock if mixture is too think. Heat through. Serve with corn tortillas and cheddar cheese.