In a large saucepan, melt butter over moderate heat. Add onion and saute until soft, about 5 minutes. Stir in flour until well mixed.
Stir in broth, zucchini, corn, chilies, and pepper. Bring the mixture to a boil over high heat, stirring occasionally. Reduce the heat; cover and simmer for 5 minutes.
Add milk; stirring frequently, heat the soup over moderate heat until it is hot but not boiling. Ladle the soup into bowls and top each serving with an equal amount of grated cheese. Serve immediately