Add 2 tablespoons butter to the skillet and cook the mushrooms until slightly browned, about 4 minutes. Stir in the Worcestershire sauce, and salt and pepper to taste, scraping up any browned bits. Sprinkle in the flour and stir, then stir in beef broth and simmer until the sauce begins to thicken, about 2 minutes. Add the remaining 1 tablespoon butter, swirling to combine.