Melt butter in a large saucepan over medium-high heat. Saute onion until transparent. Stir in the garlic, green chiles, chicken meat, and cumin. Cook for one minute to blend the flavors. Stir in the cream of chicken soup and half-and-half. Cook until heated through, about 5 minutes. Ladle hot soup into bowls. Top with cheese and a dollop of sour cream.