Combine potatoes, onion, celery, broth, and salt in a large pot on the stove or in a slow-cooker. Bring to a simmer and cook on the stove-top for about 30 minutes or in the slow-cooker for 6 hours on low/ 2-3 hours on high. Cook until the potatoes and veggies are tender.

Stir in half and half, butter, cheese, paprika, dill, and Worcestershire sauce.

Combine corn starch and water and stir into the soup.

Bring soup to a simmer on the stove-top and continue stirring until the soup is thickened. In the slow-cooker cover and set heat to high. Let cook for an additional 15-20 minutes or until the soup is thickened, stirring every so often.