Set a large saucepan over medium-high heat, then add the butter. When the butter is melted, add the onion and cook, stirring frequently for 1-2 minutes, until the onion is softened. Add the garlic and continue cooking for an additional 30 seconds.

Stir in the green chiles, cumin, and black pepper.

Add the chicken-style broth, half-and-half, and cheddar cheese. Cook, stirring frequently, for 5 minutes or until the soup is heated and the cheese is melted. Adjust seasoning to taste and serve hot.