Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish to prevent sticking. Peel and slice the potatoes into thin, even rounds about 1/8-inch thick.
In a large skillet over medium heat, cook the ground beef and chopped onion until the beef is browned and the onions are soft, about 5-7 minutes. Drain any excess grease.
Season the beef mixture with garlic powder, onion powder, salt, and black pepper. Stir well to distribute the flavors evenly throughout the meat.
Start layering the ingredients in your greased baking dish: Spread half of the sliced potatoes in an even layer on the bottom. Spoon half of the cooked ground beef mixture on top of the potatoes. Repeat with the remaining potatoes and beef.
In a small bowl, mix the cream of mushroom soup with the milk until smooth. Pour this mixture evenly over the casserole, making sure it seeps into all the layers.
Sprinkle the shredded cheddar cheese over the top. Drizzle the melted butter over the cheese to give it a golden, rich finish.
Cover the dish with aluminum foil and bake for 45 minutes. Then, remove the foil and bake for another 15 minutes, or until the cheese is bubbly and slightly golden and the potatoes are fork-tender.
Once out of the oven, let the casserole rest for about 5-10 minutes. This helps it set up and makes serving easier. Sprinkle with a little paprika for a pop of color if desired.
