In a large saucepan, arrange potatoes in a single layer. Add broth and butter. Cover and cook over medium-high heat for 12 minutes.
Uncover; cook until potatoes are tender and broth is evaporated, 7-10 minutes. Press each potato with a turner to crush slightly. Sprinkle evenly with the dill, salt and pepper. Cook until bottoms are lightly browned, 2-3 minutes longer. Serve with sour cream.