In a large pot or Dutch oven, heat oil over medium-high heat. Add onions, poblanos and diced green chiles. Saute for 10 minutes, until onions and poblanos have softened.
Add garlic and saute for 30 seconds, until fragrant.
Add chicken breasts, chicken broth, salsa verde, salt, cumin, oregano and a bay leaf. Stir to combine and bring to a boil.
Reduce heat to simmer, cover and cook for 20 minutes.
Uncover and discard bay leaf. Remove chicken from pot with a slotted spoon and transfer to a plate. Shred chicken with a fork and knife. (Leave the soup uncovered simmering on the stove while you shred the chicken.)
Add shredded chicken and beans to the pot. Bring to a boil, then remove from heat.
Stir in chopped cilantro, lime juice and serve with optional toppings, if desired.
To make in under 30 minutes, substitute the chicken breasts for leftover cooked shredded chicken or store-bought shredded rotisserie chicken. Simply saute the onions, poblanos and garlic according to the recipe and then add in all the other remaining ingredients, except the beans. Cook uncovered for 20 minutes, add in the beans and bring to a boil. Remove from heat, stir in chopped cilantro and lime juice, and serve.To make in the slow cooker, place all ingredients except beans in the slow cooker. Cover and cook for 4 hours on high or 6 hours on low. 30 minutes before it's ready, add in beans, cover and cook for 30 more minutes. Remove the chicken from the slow cooker, shred with a fork on a plate and transfer shredded chicken back to the slow cooker. Mix together and serve.To make this recipe in an Instant Pot, turn on the Sauté function and follow instructions 1-3, except don't bring to a boil. Instead, put the lid on, seal the pressure valve and cook under high pressure for 25 minutes. Do a quick pressure release, set to the Keep Warm function, discard the bay leaf and transfer the chicken to a plate and shred. Add shredded chicken back into the pot along with beans. Turn on Sauté function and bring to a boil. Turn Instant Pot off and stir in chopped cilantro and lime juice. Serve.