Add butter to stockpot. Heat over medium heat. Sauté onion and celery until onion is soft and translucent.

Stir in potatoes, carrots, ham, and chicken broth.Reduce heat to low. Simmer 20 minutes, but do not boil. If you prefer a thicker soup - puree some of the potatoes in a blender with the soup broth. Return the potatoes to the soup and stir.

Stir in half-and-half or milk, salt and pepper. Simmer 10 - 15 minutes or until heated through.

Top individual soup servings with shredded cheese and bacon crumbles.