In a large Dutch oven, heat oil over medium heat. Cook onions and poblano chiles in oil until soft. Stir in garlic, and cook for one or two minutes. Season with chile powder, cumin, and oregano.
Stir in turkey broth, cooked turkey, canned green chile peppers, cannellini beans, and hominy. Stir in water if more liquid is needed to just cover everything in the pot. Season to taste with salt and pepper. Bring to a boil, then reduce heat to low, and cover. Simmer, stirring occasionally, for about an hour to blend flavors.
