Peel and cube potatoes.

Combine potatoes with water in a large saucepan.

Bring to a boil and cook until potatoes are tender, about 12 minutes.

Drain off water.

Dice onion, celery, and carrot.

In a Dutch oven, cook onion, celery, and carrot in butter until tender.

Stir in cornstarch.

Add milk and chicken bouillon granules to the Dutch oven.

Stir in potatoes.

Cook and stir until slightly thickened.

Cook and stir for 2 minutes more.

Add cheese and stir until melted.

Add ham and heat through.

Serve topped with additional cheese.