Place a large skillet over medium heat. Add the ground beef and cook until fully browned, breaking it into crumbles as it cooks. Drain off any excess fat.
Introduce the chopped onion to the skillet and cook for approximately 3 to 4 minutes, until it becomes translucent and tender. Mix in the minced garlic and let it cook for an additional 30 seconds.
Evenly sprinkle the flour across the meat mixture, stirring to combine. Allow it to cook for 1 to 2 minutes, letting the raw flour flavor cook out.
Gradually pour in the beef broth while stirring continuously to ensure a smooth consistency without lumps. Stir in the Worcestershire sauce, along with a pinch of salt and pepper to taste.
Bring the contents to a gentle simmer. Cook for about 5 to 7 minutes, stirring now and then, until the sauce has thickened to a gravy-like consistency.
Add the butter to the skillet, stirring until fully melted and the gravy is smooth and glossy.
Serve the warm beef and gravy over a bed of mashed potatoes. Garnish with freshly chopped parsley if desired.