Preheat the oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic, sautéing until soft and translucent (about 5 minutes).
Add the ground beef to the skillet and cook until browned, breaking it apart with a spatula. Season with salt, pepper, and paprika. Drain excess fat if necessary.
In a mixing bowl, combine the cream of mushroom soup and milk. Stir until smooth.
In a large casserole dish, layer half of the sliced potatoes at the bottom. Spread half of the ground beef mixture over the potatoes, followed by half of the soup mixture. Sprinkle with ⅓ cup of cheese.
Repeat the layers with the remaining potatoes, ground beef mixture, soup mixture, and top with the remaining cheese.
Cover the casserole dish with aluminum foil and bake for 40 minutes in the preheated oven.
After 40 minutes, remove the foil and bake for an additional 10 minutes, or until the cheese is melted and bubbly, and the potatoes are fork-tender.
Remove from the oven and let it cool for a few minutes before serving. Garnish with fresh parsley if desired.