Boil 2 cups of water in a large pot, then add the diced potatoes, carrots, celery and onion. Season with salt and pepper. Cover with the lid and simmer on medium-low heat for 15-20 minutes or until the vegetables are very soft.

In a small bowl stir the cornstarch together with 3 tablespoons of water. Add the cornstarch mixture to the simmering pot and stir until the soup has thickened.

In a separate saucepan heat the milk, cheddar cheese and 1/4 cup butter until the cheese has melted. Pour the cheese mixture into the pot with the vegetables.

Add the ham. Stir until combined and warm until the soup is heated through.