Preheat oven to 350 degrees F (175 degrees C). Grease a baking dish.
Cut beef across the grain into finger-thick slices and pound with a meat mallet. Place in the baking dish in 1 layer. Season with salt and pepper. Cover with onion slices and spinkle with Cheddar cheese.
Stir together milk and mayonnaise and pour evenly over the cheese.
Bake in the preheated oven until beef is tender and cooked through, about 1 hour.