Mix together the ground beef, egg, minced onion, bread crumbs, garlic powder and salt and pepper to taste until well combined.
Preheat the oven to 350 degrees.
Form the meat mixture into four even patties, and heat the olive oil in an oven-proof skillet over medium-high heat.
Sear the patties on both sides in the heated skillet, and set aside.
In the same skillet, add the butter and reduce the heat to medium.
Add the mushrooms and onions to the skillet, and saute until becoming tender.
Stir in the minced garlic and salt and pepper to taste, and saute until 30 seconds.
Sprinkle the flour over the mixture in the skillet, and saute for 2 minutes.
Slowly whisk in the beef broth until well combined. Simmer the sauce until it begins to thicken.
Return the patties to the skillet, spoon the gravy overtop, and bake for 25-30 minutes.