Preheat the Oven: Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with olive oil or butter.
Cook the Ground Beef: In a large skillet, cook the ground beef over medium heat until browned, breaking it apart with a spatula as it cooks. Drain excess fat, if necessary, and add the diced onion. Cook for an additional 2-3 minutes until the onion becomes soft.
Prepare the Casserole Layer: In the greased baking dish, layer the thinly sliced potatoes in the bottom. Season with a little salt, pepper, and garlic powder.
Add the Beef Mixture: Spread the cooked ground beef and onion mixture over the top of the sliced potatoes. If using, add the drained green beans or mixed vegetables on top of the beef layer.
Add Soup and Cheese: In a small bowl, mix the cream of mushroom soup with a little water (about 1/4 cup) to thin it out. Pour this mixture evenly over the casserole. Sprinkle the shredded cheddar cheese on top.
Bake the Casserole: Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes. After 45 minutes, remove the foil and bake for an additional 15-20 minutes, or until the potatoes are tender and the cheese is bubbly and golden brown.
Serve and Enjoy: Let the casserole cool for a few minutes before serving. It's perfect on its own or paired with a simple side salad or bread.