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.
