Boil Mini Pierogies for 3 to 5 minutes, as directed on box.
Meanwhile, melt butter in a 3-quart saucepan over medium heat; add onions and cook until onions are softened and lightly browned, about 10 minutes, stirring occasionally. Stir in beef broth and, over high heat, bring to a boil. Simmer uncovered for 10 minutes to blend flavors. Stir in Mini Pierogies.
Preheat broiler. Spoon soup into four 1½-cup crocks or heatproof bowls; top with cheese and broil for 3 minutes or until cheese is melted. Serve.