In a large cast-iron or other heavy skillet, cook and crumble beef with onion over medium heat until no longer pink, 5-7 minutes; drain, reserving 3 tablespoons drippings. Stir in flour and seasonings until blended. Gradually stir in broth; bring to a boil. Cook and stir until thickened, 1-2 minutes.
Stir in pierogi and vegetables. Cook, uncovered, until heated through, about 5 minutes, stirring occasionally. Sprinkle with cheese.