Melt butter in a large skillet over medium heat. Saute turkey, onions, and garlic in the butter until turkey is no longer pink, 8 to 10 minutes.
While turkey is cooking, combine chile peppers, cumin, oregano, salt, and cayenne in a slow cooker set to Low. Stir in hominy and 1 can black-eyed peas. Mash the other can of black-eyed peas with a fork and stir into the slow cooker along with the chicken broth. Stir in sauteed turkey and onions.
Cook on Low until flavors combine, about 4 hours. Add cilantro just before serving.
