In a Dutch oven, heat 2 tablespoons olive oil over medium-high heat. Add chicken, chile pepper, cumin, salt, coriander, and red pepper. Cook, stirring constantly, for 8 to 10 minutes, or until browned. Remove chicken to a separate bowl.
In the same Dutch oven, heat remaining 2 tablespoons olive oil over medium heat. Add onion, poblano pepper, jalapeño pepper, garlic, and bay leaves. Cook for 4 to 5 minutes, stirring constantly, until tender.
Add reserved chicken, chicken broth, and green chiles. Bring to a boil; reduce heat to a simmer, and cook, uncovered, for 15 minutes, stirring occasionally.
Add beans; cook for 45 minutes, stirring occasionally. Remove and discard bay leaves.
Add cheese and sour cream, stirring just until cheese is melted.