In a large saucepan, saute onion and garlic in oil and butter until tender. Stir in the flour until blended. Gradually add broth. Bring to a boil; cook and stir for 2 minutes or until thickened.
Stir in the tomatoes, corn and chiles; bring to a boil. Add chicken. Reduce heat; simmer, uncovered, for 15 minutes. Add the milk, cheese and cumin. Cook and stir until cheese is melted (do not boil).