Bring first 6 ingredients to a boil in a Dutch oven. Cover, reduce heat, and simmer 15 to 20 minutes or until vegetables are tender. Remove from heat, and stir in corn.
Melt butter in a heavy saucepan over low heat; add flour, whisking until smooth. Cook 1 minute, whisking constantly. Gradually whisk in milk; cook over medium heat, whisking constantly, until mixture is thickened and bubbly. Add cheese, stirring until blended.
Stir cheese mixture gradually into vegetable mixture. Cook over medium heat, stirring constantly, until thoroughly heated. Garnish, if desired. Yield: 10 cups.