Combine potatoes, onion, 1 tablespoon salt, and 1 tablespoon pepper in a large soup pot. Cover with water; bring to a boil over high heat. Cook until the potatoes are very tender, 10 to 15 minutes. Drain potatoes, and return to pot.
Stir the milk and cubed cheese into the potatoes. Season with dill, salt, and pepper. Cook and stir over low heat until the cheese is melted, about 10 minutes.
