Bring broth potatoes, carrots, onions, and celery to boil. Reduce heat. Cover and simmer for 10 minutes. Using the back of a fork, slightly mash potatoes. Mix 1/4 cup milk and cornstarch until smooth. Stir into potato mixture. Add remaining milk. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more. Slowly stir in cheeses. Cook and stir until melted.
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