In a large saucepan or pot, combine water, potatoes, carrots, celery, and onion. Bring to boiling; reduce heat. Cover and simmer for 10 minutes.
In a medium saucepan, melt butter or margarine. Stir in flour and pepper. Add milk all at once. Cook and stir over medium heat until thickened and bubbly.
Add cheese to sauce and cook and stir until melted. Add cheese sauce to vegetable mixture. Stir in corn and ham. Heat through, but don't boil. Ladle into soup bowls and top with additional pepper, if you like. Makes 6 main-dish servings.
Reduce the fat and sodium in this cheesy soup by using less cheese and ham.