1. Preheat your oven to 400°F (200°C). Grease a 9×13-inch baking dish with the tablespoon of butter, ensuring the sides and bottom are well-coated.
2. In a medium saucepan, combine the heavy cream, milk, garlic, salt, pepper, and nutmeg. Bring to a gentle simmer over medium heat, stirring occasionally.
3. Layer half of the sliced potatoes in the prepared baking dish. Pour half of the cream mixture over the potatoes, ensuring even coverage.
4. Sprinkle half of the Gruyere and Parmesan cheeses over the potatoes.
5. Repeat with the remaining potatoes, cream mixture, and cheeses, finishing with a generous layer of cheese on top.
6. Cover the dish with foil and bake in the preheated oven for 45 minutes.
7. Remove the foil and continue baking for an additional 15-20 minutes, or until the top is golden brown and crispy.
8. Allow the gratin to cool for at least 10 minutes before serving. This helps the flavors meld together beautifully.

As you prepare this dish, remember the joy of creating something from scratch, a lesson I learned from my grandmother’s intuitive cooking style. Taste, adjust, and most importantly, enjoy the process.