Hamburger steak smothered in brown gravy with mushrooms and onions

Hamburger steak smothered in brown gravy with mushrooms and onions was my hubbies request for dinner last night.
Ingredients
2 lbs Ground Chuck
1 Yellow Onion thinly sliced
16 oz mushrooms I used a blend of cremini and shitaki
2 cups beef broth – divided. I use canned fat-free low sodium
2 tbsp all-purpose flour
6 tbsp butter
4 sliced scallions white and green sections
salt and pepper to taste
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Instructions
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.