**1. Prepare the Potatoes:**
- Preheat your oven to 375°F (190°C).
- Use a mandoline slicer or sharp knife to slice the potatoes evenly, about ⅛ inch thick.
**2. Make the Cream Sauce:**
- In a medium saucepan, melt the butter over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.
- Stir in the flour, whisking constantly, and cook for another minute to make a roux.
- Gradually whisk in the milk and heavy cream, ensuring there are no lumps. Cook until the mixture thickens slightly, about 3-4 minutes.
- Stir in the Parmesan cheese, salt, pepper, nutmeg (if using), and basil. Remove from heat.
**3. Assemble the Dish:**
- Grease a 9x13-inch baking dish. Layer half of the sliced potatoes evenly in the dish. Pour half of the cream sauce over the potatoes, spreading it evenly.
- Add the remaining potatoes and pour the rest of the cream sauce on top. Sprinkle the shredded mozzarella or Gruyere cheese over the top layer.
**4. Bake:**
- Cover the dish with aluminum foil and bake for 40 minutes. Remove the foil and bake for an additional 20-25 minutes, or until the potatoes are tender and the top is golden and bubbly.
**5. Garnish and Serve:**
- Let the dish rest for 10 minutes before serving. Garnish with additional fresh basil if desired.