Melt butter in the skillet over medium heat. Cook and stir onion and garlic in hot butter until softened, 3 to 5 minutes. Stir flour into onion mixture; cook and stir until flour is browned, about 1 minute. Return beef to the skillet; stir. Pour beef broth over the mixture in the skillet; bring to a boil. Stir Worcestershire sauce and mustard through the mixture.