Start by heating a large pot over medium heat. Add butter, then toss in the diced onion and carrot. Sauté these for about 10 minutes, stirring often, until they’re soft and slightly golden. Add in the garlic and let it cook for just one more minute—garlic burns fast, so keep an eye on it.
Pour in your chicken broth and bring the mixture to a gentle simmer. Cut the cream cheese into cubes and drop them in one at a time, stirring continuously to ensure it melts smoothly. Then slowly add the cheddar and pepper jack cheeses, about ½ cup at a time. Stir after each addition to help the cheese fully melt without clumping.
Once your cheese is completely incorporated, it’s time to stir in the diced green chiles, cooked chicken, chili powder, and black pepper. Let it all simmer together for 5 to 7 minutes so the flavors can blend. Taste the soup, and add more salt or pepper if needed.
If the soup feels too thick, add a bit more chicken broth. For a creamier finish, I sometimes stir in ½ cup of heavy cream—especially when I want that extra-rich feel.
Ladle the soup into bowls and top with freshly chopped cilantro, extra shredded cheese, and crispy tortilla strips. You can even add a dollop of sour cream or a few avocado slices for bonus flavor!