Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish with olive oil or butter.
Heat a large skillet over medium heat. Add the ground beef and chopped onion, cooking until the beef is browned and the onion is tender. Drain any excess grease.
Stir in the minced garlic, salt, black pepper, and paprika. Cook for 1 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 evenly over the beef.
Sprinkle with 1 cup of the shredded cheddar cheese.
Repeat the layers with the remaining potatoes, beef mixture, and soup mixture.
Top with the remaining cheddar cheese and the mozzarella cheese, if using.
Cover the baking 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 tender and the cheese is melted, bubbly, and lightly golden.
Let the casserole rest for 5 minutes before serving.