In a large stock pot, combine the potatoes, water, celery, carrots, onion, and bouillon. Bring to a boil. Reduce heat; cover and simmer for 10-12 minutes or until potatoes are tender.
Add 1 1/4 cup on the milk to the vegetable mixture.
In a small bowl, whisk together the remaining 1 cup of milk until smooth. Slowly add the flour/milk mixture into vegetable mixture while stirring. Bring to a boil; cook and stir for 2 minutes or until thickened.
Reduce heat to low; stir in parsley, salt, pepper, and cheese until cheese is melted.