In a large pot over medium heat, melt butter. Add onion, celery and garlic, and cook until vegetables are softened, about 5 minutes.
Add chicken broth, potatoes, ham, thyme, and black pepper. Bring to a boil, reduce heat to low and simmer for 15 minutes, or until potatoes are tender.
Stir in half-and-half and heat through. Serve hot.
Interesting Facts
Potatoes are a great source of potassium, vitamin C, and fiber.
Ham is a great source of protein.
Half-and-half is a combination of half whole milk and half light cream.