Heat a skillet over medium heat and cook the ground turkey until it is no longer pink, breaking it up as it cooks. Drain any excess liquid.
Add the diced poblano peppers, onion, and garlic to the skillet. Cook for 3 to 4 minutes until the vegetables start to soften.
Transfer the turkey mixture to the slow cooker. Stir in the white beans, diced tomatoes, chicken broth, cumin, chili powder, oregano, salt, and black pepper.
Cover and cook on low for 6 hours or on high for 3 hours.
Taste and adjust salt or pepper if needed. Serve hot with chopped cilantro and lime wedges on the side.