In a large bowl, gently combine beef, oats, Worcestershire, ½ teaspoon salt, ¼ teaspoon pepper, garlic powder, onion powder and milk. Shape into 4 ½-inch thick oval patties and place on a parchment-lined tray. Cover loosely and refrigerate for at least 30 minutes, or overnight.
Melt 1 tablespoon of butter in a large skillet over medium-high heat. Fry the patties until browned on both sides (about 3 minutes per side). Transfer to a plate.
Melt remaining 3 tablespoons of butter in the skillet over medium-high heat. Add onion and cook until softened, about 5-7 minutes. Add mushrooms and ½ teaspoon salt and cook for about 5 more minutes. Stir in tomato paste and flour; cook for 2 minutes. Gradually pour in the broth and wine, stir constantly. Bring to a simmer.
Return the browned patties to the skillet. Cover, reduce the heat to medium-low, and cook for 12-15 more minutes, or until the patties are cooked through. Taste and season the gravy with salt and pepper, if necessary.
Notes
Have leftovers? Wrapped properly, the cooked patties and gravy will stay fresh in the refrigerator for at least 2-3 days. You can even freeze the cooked steaks and gravy for up to 3 months.