Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Slice the potatoes thinly and evenly.
Cook the Ground Beef: In a large skillet over medium heat, cook the ground beef and chopped onion until the beef is browned (5-7 minutes). Drain excess grease.
Season Beef: Season the beef mixture with garlic powder, onion powder, salt, and black pepper. Stir well.
Assemble - Layer 1: Spread half of the sliced potatoes in an even layer on the bottom of the baking dish.
Assemble - Layer 2: Spoon half of the cooked ground beef mixture on top of the first potato layer.
Assemble - Layer 3 & 4: Repeat the layers with the remaining potatoes and beef mixture.
Make the Sauce: In a small bowl, mix the cream of mushroom soup with the milk until smooth. Pour this mixture evenly over the casserole.
Top and Butter: Sprinkle the shredded cheddar cheese over the top. Drizzle the melted butter over the cheese.
Bake Covered: Cover the dish with aluminum foil and bake for 45 minutes.
Finish Bake: Remove the foil and bake for another 15 minutes, or until the cheese is bubbly and golden brown.
Rest and Serve: Let the casserole rest for 5-10 minutes before serving. Sprinkle with paprika for garnish if desired.