In a large pot, combine the potatoes, onion, celery, and bouillon cubes. Add enough water to cover them. Bring to a boil, then simmer gently for 15 minutes.
Add the half-and-half cream, bacon, mushroom soup, and stir well until they blend. Then add the shredded cheddar and continue stirring until it completely melts.
Let the soup simmer on low heat until the potatoes are fully cooked and tender.
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