Place ham, celery, onion, carrots, potatoes, corn and chicken broth in crock pot. Add salt and pepper to taste. (The ham will provide some salt.) If cooking stovetop, cook until potatoes are done. Turn crock pot to low and cook 3 to 4 hours.
During last 10 minutes of cooking add evaporated milk. Heat only-do not boil. Str lightly to allow cheese to melt. If a thicker soup is desired, add optional cornstarch after dissolving it in cold water. Smash a few potatoes for thickening.