In a large bowl, add the 1 ½ pounds ground beef, 1 large lightly beaten egg, 1 teaspoon salt, ½ teaspoon ground black pepper, 2 minced garlic cloves, and 1 tablespoon Worcestershire sauce. Mix the meat mixture using a large spoon or clean/gloved hands, until combined.
Divide the ground beef mixture and form 4 to 5 oval-shaped patties that are about ½-inch thick and 3 to 4 inches wide. Set them aside.
Heat a large nonstick skillet or cast iron skillet over medium-high heat, you can add some 2 tablespoons olive oil but it isn't necessary. After 1 to 2 minutes, add the burger patties careful not to overcrowd the pan.
Cook for 4 to 5 minutes, flip each pattie to the opposite side, and continue cooking for another 4 to 5 minutes. The patties should have browned and the internal temperature has reached 160 degrees F.
Carefully remove each hamburger from the skillet onto a plate and cover loosely (tent) with aluminum foil. Repeat the process until all of the patties are done.
Reduce the heat to medium heat. Using the same skillet with the ¼ cup pan drippings, add the 3 tablespoons all-purpose flour and stir it continuously for 4 to 5 minutes, until it's dark brown and forms a paste consistency.
Slowly add in the 2 cups beef broth and 1 beef bouillon cube. Stir to combine and allow the gravy mixture to come to a low boil and simmer for about 3 minutes.
Return the hamburger steaks to the skillet with the gravy. Spoon the brown gravy over the hamburger steaks. Cook for an additional 5 minutes. Remove the hamburger steaks and gravy from the skillet. Serve warm over mashed potatoes, rice, or egg noodles. Enjoy!