Heat the butter in a medium saucepan over medium-low heat, then cook the minced garlic in it for about 1 minute. Look for pale golden edges and a fragrant garlic aroma rather than deep browning.
Whisk the flour into the butter for 1 minute, gradually incorporate the broth, bring to a simmer while whisking for several minutes, then take the pan off the heat and mix in the chili powder, cumin, garlic powder, salt, and pepper to taste before setting it aside. The finished sauce should look smooth and thickened, without visible flour pockets.
Arrange the chicken breasts in a large slow cooker, distribute the Rotel and jalapeno over them, add the prepared sauce, and cook with the lid on for 4 hours on low. The chicken should be cooked through and tender enough to pull apart without becoming dry or stringy.
Lift the chicken onto a cutting board, mix the Colby Jack into the liquid, replace the lid while pulling the meat into large pieces, and return those pieces to the cooker. The covered broth gives the cheese a warm environment to soften while the chicken retains its chunky texture.
Continue cooking with the lid on for 15 minutes, then thoroughly stir the soup. The cheese should have melted into the broth and the chicken should be hot throughout.
Break tortilla chips into individual bowls, spoon the soup over them, and finish with additional cheese and optional cilantro. The chips provide crunch against the creamy broth, while the herbs add freshness.