Heat olive oil in a large skillet over medium heat. Cook and stir onion, celery, and poblano peppers in the hot oil until tender, 5 to 10 minutes. Add garlic, cumin, coriander, and cayenne pepper to onion mixture; cook and stir until garlic is fragrant, about 1 minute.

Mix turkey into onion mixture; cook and stir until turkey is cooked through and no longer pink, 5 to 7 minutes. Add chicken broth, cannellini beans, and oregano to turkey mixture; cover skillet and cook for 15 minutes. Stir hominy and salt into chili and continue cooking until heated through, about 15 minutes more.