Cook onions and garlic. In a large pot or Dutch oven, melt butter over medium-low heat. Add chopped onion and cook for 7-10 minutes until onions look more translucent and are tender, stirring occasionally and watching the heat to make sure the onion doesn’t burn. Add garlic and cook an additional 1-2 minutes, stirring occasionally. Add in flour and stir to break up any clumps. Cook for an additional 2-3 minutes.
Add broth, base, beans, and seasoning. Slowly pour in and whisk chicken broth into the onion mixture. Add the chicken bouillon base and whisk to combine. Stir in chili powder, cumin, salt, pepper, coriander, garlic powder, and cayenne. Add the beans, green chilis, and salsa verde, and turn heat up to medium-high heat. Bring soup just to a boil.
Add corn, chicken, and lime. Lower heat to a simmer and add corn, chicken, and lime juice until the ingredients are warmed through, about 5-10 minutes.
Add cream cheese. Put cream cheese in a bowl and microwave for 30 seconds. Spoon some broth from the soup into the bowl and whisk cream cheese until smooth. Turn off heat for the soup. Stir in whisked cream cheese, cream, and chopped cilantro.
Serve. Serve chili warm in individual bowls and top with desired toppings.