1. Preheat the oven to 375°F (190°C) and grease a 9×13-inch baking dish with butter.

2. In a saucepan over medium heat, warm heavy cream, milk, and minced garlic until steaming but not boiling.

3. Season the cream mixture with salt, pepper, and nutmeg, then remove from heat and stir in half of the Gruyere and cheddar until melted.

4. Arrange a layer of mixed sliced root vegetables in the baking dish, slightly overlapping each slice.

5. Pour a portion of the cheese cream over the first layer and sprinkle with Parmesan.

6. Repeat layering vegetables, cheese cream, and Parmesan for three to four layers, alternating vegetable colors.

7. Cover the dish with foil and bake for 45 minutes, allowing vegetables to soften.

8. Remove the foil and bake for an additional 20–25 minutes until the top is golden and bubbling.

9. Let the gratin rest for 10–15 minutes before slicing to allow layers to set.

10. Serve warm, garnished with fresh thyme or chives if desired.