Preheat the oven to 375°F (190°C).
Wash and peel the potatoes. Using a mandoline or a sharp knife, slice the potatoes into thin, even rounds (about ⅛ inch thick).
In a mixing bowl, combine the heavy cream, minced garlic, salt, black pepper, and paprika. Whisk together until well combined.
Layer half of the sliced potatoes in the bottom of the 9x13 inch baking dish. Pour half of the cream mixture over the potatoes and sprinkle with half of the cheddar cheese.
Repeat the layering process with the remaining potatoes, cream mixture, and cheese.
Cover the baking dish with aluminum foil and place it in the preheated oven. Bake for 45 minutes.
After 45 minutes, remove the foil and bake for an additional 15 minutes, or until the top is golden brown and the potatoes are tender.
Remove from the oven and let it rest for 10 minutes. Garnish with chopped parsley before serving.