Preheat the oven to 400°F. In a mixing bowl, combine the cheddar cheese soup, evaporated or whole milk, and heavy cream until well blended, then set aside. Clean and dry the potatoes thoroughly. Using a mandoline or sharp knife, slice them into 1/8-inch thick rounds.

Heat a 12-inch skillet over medium-high heat and cook the ground beef along with the diced onion until browned. Incorporate the garlic, salt, black pepper, and paprika, cooking for an additional minute. Drain any excess fat and transfer the beef mixture to a plate.

Begin layering in an oven-safe skillet or baking dish: start with a layer of sliced potatoes, then spread one-third of the cheese sauce over them, followed by one-third of the cooked ground beef. Repeat this layering process two more times, reserving the shredded cheese for later.

Cover the dish with foil and bake for 1 hour, or until the potatoes are tender when pierced with a fork. Remove the foil, top with the shredded cheddar cheese, and return to the oven for another 10 minutes until the cheese is fully melted.

Allow the casserole to rest for 10 minutes after baking. Garnish with chopped parsley before serving.