In large saucepan, heat butter or margarine over medium heat. Add celery and onions; cook and stir until tender.
Add potatoes and broth, and simmer until tender.
Stir in milk, and season with salt and pepper. Dissolve cornstarch in 1/4 cup water, and slowly stir into soup. Bring to a boil for 1 minute, and then turn heat to medium-low. Stir in 2 cups cheese, and continue stirring until it melts. Serve.