Combine the ground beef, egg, breadcrumbs, minced onion, garlic, Worcestershire sauce, kosher salt, and black pepper in a bowl. Mix only until the ingredients are combined so the finished meatballs stay tender.

Shape the mixture into approximately 16 meatballs, each about 1 1/2 inches in diameter. Keep the portions similar in size so they cook evenly.

Heat a large skillet over medium to medium-high heat and add the butter or neutral cooking oil. Brown the meatballs on several sides, working in batches if necessary, then transfer them to a plate; they do not need to be fully cooked yet.

Add the sliced mushrooms and thinly sliced onion to the same skillet. Cook for 5 to 7 minutes, until the mushrooms release their liquid and begin to brown and the onion softens.

Sprinkle the flour over the mushrooms and onion and stir for 1 minute. Gradually whisk in the beef broth, Worcestershire sauce, and Dijon mustard if using, scraping the browned bits from the skillet.

Return the meatballs and any accumulated juices to the skillet. Reduce the heat, partially cover, and simmer for 10 to 15 minutes, turning the meatballs once, until the gravy thickens and the meatballs reach 160°F (71°C) in the center.

Taste the gravy and season with additional salt and black pepper as needed. Garnish with chopped fresh parsley and serve immediately over mashed potatoes, egg noodles, rice, or buttered noodles.