Set your oven to 375°F (190°C). Grease a 9×13-inch casserole dish generously with butter or cooking spray to ensure easy serving later.
In a medium saucepan, combine the heavy cream, milk, minced garlic, salt, black pepper, and smoked paprika. Heat the mixture over medium heat, whisking occasionally to prevent the milk from scalding.
Using a mandoline slicer or sharp knife, slice the potatoes into even, thin rounds.
Arrange half of the potato slices in overlapping layers at the bottom of your prepared casserole dish.
Sprinkle half of the shredded Gruyère and Parmesan cheese evenly over the potato layer. Pour half of the warm cream mixture on top, ensuring it seeps into the layers.
Layer the remaining potatoes in the same manner, followed by the rest of the cheese and cream mixture.
Scatter small cubes of butter across the top layer. This step helps achieve a beautifully golden and crisp crust.
Cover the casserole tightly with aluminum foil and bake in the preheated oven for 45 minutes.
After 45 minutes, remove the foil and bake for an additional 15 minutes. The top should turn golden brown, with bubbling cheese along the edges.