In a bowl, combine the ground beef, bread crumbs, ½ onion (grated), garlic powder, onion powder, 1 teaspoon kosher salt (use half for table salt), pepper, and egg. Mix until all ingredients are evenly distributed.
Divide the mixture into 6 equal portions and shape them into thin patties.
Add a thin coating of oil to a skillet over medium-high heat. Once hot, place the patties in the skillet. Cook until browned on both sides, about 2-3 minutes per side.Adjust the cooking time to your desired level of doneness. Transfer to a plate and set them aside. In a bowl, combine the beef base, 3 cups of warm water, soy sauce, and Worcestershire sauce. Mix until the beef base is fully dissolved.
In the same skillet over medium-high heat, spread the mushrooms in an even layer. Let them sit without stirring initially to sear them nicely and let their moisture evaporate so the sauce doesn't end up watery.Stir the mushrooms after a few minutes, then add the butter, onions, and garlic. Lower the heat and sauté until the onions and garlic are softened. Sprinkle the all purpose flour over the mushrooms and aromatics. Stir so the flour cooks evenly, about a minute.
Pour in the beef broth mixture while stirring constantly to prevent lumps. Turn up the heat and cook until the gravy thickens. Add some ground pepper and adjust the taste as needed.
Place the burger patties in the gravy and spoon the sauce over them to ensure even coating. Cook until heated through, then turn off the heat.