Divide meat into 6 equal-sized patties. Salt and pepper each side liberally.
Melt 2 tablespoons of butter in the skillet. Add the onion and mushrooms and cook over medium heat until browned. Remove from the pan and set aside
Melt 2 additional tablespoons of butter in the skillet and sear the beef patties 3 minutes on each side or until beef reaches 120°F. Remove from the skillet.
Add the last 2 tablespoons of butter to the skillet. Add 1½ cups beef broth. Bring to a simmer and whisk in the flour. Cook until thickened. If the gravy gets too thick, add the remaining 1/2 cup of broth.
Add beef patties, mushrooms and onions back to the hot gravy. Salt and pepper to taste. Cook until desired doneness.
Serve and garnish with sliced scallions.
