Heat 1 teaspoon of the oil in a large soup pot or Dutch oven over medium-high heat. When the oil shimmers, add the bison and cook until browned, taking care not to break the meat into very small pieces, about 10 minutes. Transfer the bison to a plate using a slotted spoon and set aside. Drain the liquid in the bottom of the pot and discard.
Keep the pot over medium-high heat and add the remaining 1 teaspoon oil, the poblano peppers and onions. Cook until softened and beginning to brown, about 5 minutes. Add the chili powder, coriander, cumin, salt, cayenne pepper and garlic. Cook and stir until the spices are fragrant and toasted, 1 to 2 minutes. Add the tomatoes with the juices, and bring to a simmer while scraping any browned bits off the bottom of the pan, about 2 minutes.
Return the bison to the pot and add the black beans, kidney beans, hominy and 4 cups water. Bring to a boil, and then reduce the heat, cover and simmer until thickened, about 45 minutes. Season with salt. Serve with the sour cream, cheese, cilantro, onions, lime and avocados, if desired.