Heat the olive oil in a large pot or dutch oven over medium heat. Add the onion and poblano peppers and cook until fragrant, about 8 minutes. Stir in garlic, parsley, dill, paprika, and a large pinch of salt and pepper. Cook 5 minutes, until very fragrant. Add the shredded chicken and chicken broth. Bring to a simmer and cook for about 6 minutes.
Stir in the cream cheese until smooth. Add the beans, salsa verde, hot sauce, and cheddar cheese. Cook 5-10 minutes until heated through. Remove from heat, and stir in the cilantro. Taste for seasoning.
Ladle into bowls and serve with tortilla chips, avocado and extra cheddar cheese.