Heat olive oil in a large pot or Dutch oven over medium-high heat. Add onion, poblano peppers, jalapeño, and green chiles. Sauté for about 10 minutes until softened.
Add minced garlic and cook for another minute.
Pour in chicken broth, then stir in shredded chicken, salsa verde, cannellini beans, corn, salt, cumin, oregano, and bay leaf. Bring to a gentle boil.
Reduce heat to low, cover, and let simmer for 20 minutes.
Uncover and cook for an additional 10 minutes to reduce the broth slightly. Remove bay leaf and stir in cilantro and lime juice.
Serve in bowls with desired toppings.
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Notes
Store in airtight containers in the refrigerator for up to 4 days. Reheat on the stove over medium heat.