Heat olive oil in dutch oven over medium heat.
Add the onion and cook until fragrant, about 5 minutes.
Stir in the garlic, poblano peppers, cumin, paprika, chili powder, and a pinch each of salt and pepper. Cook 5-10 minutes, until very fragrant.
Add the chicken, then add in 4 cups broth. Season with more salt and pepper. Partially cover and simmer over medium-low heat for 20 minutes, until the chicken is cooked through.
Melt the cream cheese in the microwave for 10-15 seconds.
Pull the chicken out and shred using mixer or 2 forks. Stir in the cream cheese until smooth, then stir in the shredded chicken, white beans, salsa verde, and cheddar cheese. Cook 5-10 minutes, until the cheese is melted.
Remove from the heat and stir in the cilantro. If needed, thin with additional broth.
Top, as desired, with yogurt/sour cream, cheese, avocado, cilantro, or green onions. Squeeze lime over each bowl.
