Preheat your oven to 350°F (175°C) and grease a 9×13-inch baking dish with olive oil or butter.
Heat a large skillet over medium heat. Cook the ground beef with the chopped onion until browned. Drain excess fat if necessary.
Stir in the minced garlic, salt, pepper, and paprika. Cook for another minute until fragrant.
In a medium bowl, whisk together the cream of mushroom soup and milk until smooth.
Arrange half of the sliced potatoes in an even layer in the prepared baking dish.
Spread half of the beef mixture over the potatoes.
Pour half of the soup mixture over the beef and sprinkle with 1 cup of shredded cheddar cheese.
Repeat with the remaining potatoes, beef mixture, soup mixture, and finish with the remaining cheddar and mozzarella cheese.
Cover tightly with aluminum foil and bake for 45 minutes.
Remove the foil and continue baking for 15–20 minutes, or until the potatoes are tender and the cheese is bubbly and golden.
Let the Cheesy Hamburger Potato Casserole rest for 5 minutes before serving.