Heat the oil in large pot or Dutch oven over moderate heat. Add the onion, celery, poblanos, and cook, stirring occasionally, until the vegetables are soft, about 8 minutes. Add the garlic, cumin, coriander and cayenne and cook, stirring, until fragrant, about 30 seconds.
Add the ground turkey and cook, breaking up the meat with a spoon, until the meat is no longer pink about 2 minutes. Add the white beans, broth and oregano. Cook, partially covered, stirring occasionally, for 25 minutes.
Add the hominy and salt and more cayenne pepper, to taste, and continue cooking, partially covered, 10 minutes longer. Ladle into individual bowls and top each serving with 1 tablespoon of yogurt and 1 1/2 teaspoons of cilantro. Garnish with a lime wedge.