Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking dish with olive oil or butter.
In a large skillet over medium heat, cook the ground beef and chopped onion until the meat is browned and fully cooked. Drain excess fat if needed.
Stir in the minced garlic, salt, black pepper, and paprika. Cook for another minute until fragrant.
In a separate bowl, whisk together the cream of mushroom soup and milk until smooth.
Arrange half of the sliced potatoes evenly in the prepared baking dish.
Spread half of the beef mixture over the potatoes.
Pour half of the soup mixture over the beef, then sprinkle with 1 cup of shredded cheddar cheese.
Repeat the layers using the remaining potatoes, beef mixture, and soup mixture. Finish with the remaining cheddar cheese and mozzarella cheese.
Cover the dish tightly with aluminum foil and bake for 45 minutes.
Remove the foil and continue baking for 15–20 minutes, or until the potatoes are fork-tender and the cheese is bubbly and golden brown.
Let the Cheesy Hamburger Potato Casserole rest for about 5 minutes before serving.
Serve warm with a crisp green salad, steamed vegetables, or fresh dinner rolls.