Add butter to a large pot or Dutch oven. Place over medium heat.
When butter has melted and is hot (do not burn), add onion, garlic, red bell pepper and green bell pepper. Cook, stirring frequently, until softened, about 5 minutes.
Stir in chili powder, cumin, smoked paprika and cayenne pepper.
Sprinkle flour over the vegetable mixture. Cook, stirring constantly, for 1 to 2 minutes to remove the raw flour taste.
Gradually whisk in chicken broth until smooth. Bring to a simmer.
Stir in half-and-half and diced tomatoes with green chilies. Simmer for 10 minutes, stirring occasionally.
Stir in shredded chicken and frozen corn. Simmer for another 5 minutes until heated through.
Reduce heat to low.
Gradually stir in cheddar and Monterey Jack cheeses. Continue to stir until cheese is completely melted and soup is creamy.
Taste. Season with salt and pepper, to taste.
Ladle soup into bowls.
Top with tortilla strips, fresh cilantro, lime wedges, sour cream and additional cheese, as desired.