Cut mushrooms in thick slices. Slice half of the onion, and chop the other half in small chunks.
Lightly oil the skillet on medium heat. Insert chopped onions and season with salt and pepper. Stir fry until translucent and set aside to cool.
In a medium bowl mix together ground beef, seasoning ingredients, and cooked onions and mix well. Split into 4 patties. Flatten each patty, insert mozzarella cheese and roll into a flat ball shape. Push the center of the patty slightly inwards for even cooking.
Prepare some oil in a skillet on medium heat, and cook both sides of the patties, flipping occasionally. Once they have browned, adjust the heat to low and cover the skillet, cooking gently until the insides are fully cooked.
In a separate saucepan, melt the butter on medium heat, insert sliced onion and mushroom and stir-fry for 2 minutes. Insert sauce ingredients and boil gently until it becomes a thick consistency.
Plate the hamburg steak and pour the sauce on top. Serve with grilled vegetables, mashed potatoes and/or rice on the side.