Sear chicken: Heat 2 tablespoons oil over medium-high heat in a large Dutch oven/soup pot. Season chicken with 1/2 teaspoon salt and 1/2 teaspoon pepper then sear until golden, about 2 minutes per side. Remove to a plate but leave drippings.
Sauté aromatics: Melt 2 tablespoons butter with 1 tablespoon olive oil over medium low heat. Once melted, increase to medium-high heat and add onions and jalapenos; cook for 5 minutes. Add garlic and cook 30 seconds.
Cook roux: Sprinkle in flour and cook one additional minute while stirring (it will be thick).
Add ingredients: Add chicken back to the pot followed by beans, creamed corn, corn, salsa verde, chicken bouillon and all seasonings. Whisk cornstarch with 1 cup of chicken broth and stir in. Add remaining chicken broth.
Simmer: Cover the soup to bring to a boil then uncover and simmer for 12-15 minutes or until chicken is tender enough to shred, stirring often so the bottom doesn't burn. Remove chicken to a cutting board, shred, then stir back into the soup. Stir in half and half and cilantro and warm through.
Season to taste: Add additional half and half or broth to thin to desired consistency if you like. Season with salt / pepper / cayenne pepper to taste. Serve with sour cream, crushed tortilla chips, chopped avocados and cilantro.