Preheat your oven to 400°F (200°C).
In a medium mixing bowl, whisk together the condensed cheese soup, evaporated milk, and heavy cream until smooth. Set the mixture aside.
Wash and dry the potatoes, then slice them into 1/8-inch-thick rounds using a sharp knife or mandoline slicer.
Heat a 12-inch oven-safe skillet over medium-high heat. Add the ground beef and chopped onion, cooking until the beef is browned and the onion is softened. Stir in the garlic, salt, black pepper, and paprika, then cook for another minute until fragrant. Drain any excess grease and transfer the beef mixture to a plate.
Arrange a layer of sliced potatoes in the skillet or a greased baking dish. Spoon about one-third of the cheese sauce over the potatoes, then top with one-third of the cooked beef mixture.
Repeat the layers two more times, finishing with the remaining cheese sauce on top. Do not add the shredded cheese yet.
Cover the dish with foil and bake for 1 hour, or until the potatoes are tender when pierced with a fork.
Remove the foil, sprinkle the shredded cheese evenly over the top, and return the dish to the oven. Bake for another 10 minutes, or until the cheese is fully melted and bubbly.
Let the casserole rest for about 10 minutes before serving. Garnish with freshly chopped parsley, if desired, and enjoy.