Do not wash the skillet. Let it cool a bit, then place it over medium heat and add the butter.
When the butter is melted and foaming add the onions and mushrooms. Cook for 5 minutes until the onions start to soften. Stir occasionally while gently scraping any bits off the bottom of the skillet.
When most of the liquid has cooked out, sprinkle the flour over the mushrooms. Stir well to combine. Cook the flour for 2-3 minutes, stir almost constantly.
Slowly add the beef broth to the mushroom mixture while stirring and gently scrapping the bits off the bottom of the pan. Continue stirring until the broth is incorporated and the sauce is smooth.
Add the Worcestershire sauce and stir.
Raise the heat to medium-high and bring the mushroom sauce to a simmer, lower the heat to medium-low and cover the skillet. Cook the gravy for 10 minutes. Uncover the skillet and cook an additional 5 minutes until the gravy thickens. Stir occasionally and keep the sauce at a simmer, raise or lower the heat just a bit, as needed.
Taste the mushroom sauce and add salt if needed. As a reference, we added ¼ teaspoon to ours.
Add the steaks back to the skillet. Turn to coat with the sauce. Lower the heat to low, cover and let them sit in the gravy for a minute or two until warmed through.
Serve with your side dish of choice.