In a large saucepan, bring potatoes, carrot, celery, onion, chicken broth and salt to a boil. Reduce heat; cover and simmer until potatoes are just tender. Do not drain; mash slightly. Stir in milk. In a small bowl, blend butter, flour, parsley and pepper; stir into potato mixture. Cook and stir over medium heat until thickened and bubbly. Remove from heat; add cheese and stir until cheese is almost melted. Let soup stand for 5 minutes.

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