1. Heat a skillet over medium heat and add ground beef. Cook, stirring frequently to break it apart, until browned (around 5-7 minutes). Drain any excess fat.
2. Add chopped onion and minced garlic to the skillet with the ground beef. Sauté until the onion becomes translucent (about 3-5 minutes).
3. Sprinkle flour evenly over the beef and onion mixture. Stir well to coat the ingredients, allowing the flour to cook for 2 minutes to eliminate the raw taste.
4. Gradually pour in beef broth while stirring continuously to prevent lumps. Bring the mixture to a simmer until it thickens to a gravy consistency. Optionally, add Worcestershire sauce for enhanced flavor.
5. While the gravy simmers, peel and dice potatoes. Boil them in a large pot of water until fork-tender (approximately 10-15 minutes).
6. Drain the cooked potatoes and return them to the pot. Add butter and milk, then mash until smooth. Season with salt and pepper to taste.
7. For serving, spoon a generous amount of mashed potatoes onto each plate. Top with the warm ground beef and gravy mixture. Garnish with minced chives or parsley if desired.
8. Enjoy your comforting meal of Ground Beef and Gravy Over Mashed Potatoes!