Preheat Your Oven: Set your oven to 375°F (190°C) and grease a 9x13-inch baking dish.
Cook the Ground Beef Heat olive oil in a skillet over medium heat. Add the ground beef, breaking it up with a spatula as it cooks. Toss in the onion and garlic, cooking until the beef is browned and the onion is soft. Season with salt, pepper, paprika, and thyme. Remove from heat and set aside.
Layer the Ingredients Arrange half of the sliced potatoes in a single layer at the bottom of the prepared baking dish. Spread half of the ground meat mixture atop the potatoes. Repeat with the remaining potatoes and beef.
Sauce Preparation: Combine the cream of mushroom soup and milk in a bowl until you achieve a smooth consistency. Pour the mixture evenly over the layered potatoes and beef.
Add Cheese and Bake: Cover the casserole with foil and bake for 45 minutes. Remove the foil, sprinkle shredded cheese on top, and bake for another 15 minutes or until the cheese is bubbly and golden.