In a large mixing bowl, add the finely chopped onion, bread crumbs, ground beef, eggs and seasonings. Using your hands, mix the ingredients together thoroughly.
Heat a large, wide skillet over medium heat. Add 2 T olive oil to the pan.
Divide the ground beef mixture into five portions. Shape each portion into an oblong patty about 3/4″ thick.
Add the patties to the pan, and allow to brown- do not move them or attempt to turn them until a nice brown crust has formed (3-4 minutes). Flip over and brown the other side. Remove from the pan and set aside.
Add 1 T butter and mushrooms to the pan. Saute until golden brown. Add the remaining 2 T butter. Sprinkle the flour over when melted, then whisk in flour. Cook for 1 minute, then slowly add in the stock. Whisk until no flour lumps remain.
Simmer until the gravy has thickened slightly, then return patties to the pan and allow them to finish cooking in the sauce. Serve steaks alongside mashed potatoes, topped with the mushrooms and gravy.