1. In a heavy skillet, cook the onion in the oil over moderately low heat, stirring, until it is softened. Stir in the bell pepper, potatoes, zucchini and corn. Cook the mixture, stirring, for 3 minutes.
2. Add the broth in a stream, stirring, and stir in the milk, cayenne pepper, salt and black pepper. Bring the mixture to a boil and simmer it, uncovered, stirring occasionally, until it is thickened.
3. Add the Cheddar cheese in 5 batches, stirring after each addition until it is melted, but do not let the soup come to a boil or the cheese will separate.