Preheat your oven to 400°F (200°C) and grease a 3-quart baking dish with unsalted butter.

Slice sweet potatoes, parsnips, and beets into very thin rounds using a mandoline.

Mix sliced sweet potatoes and parsnips with 4 tablespoons of heavy cream, ½ ounce of grated Parmesan, and 1 teaspoon of fresh thyme in separate bowls. For beets, use 2 tablespoons of cream and ½ ounce of Parmesan. Season with salt and pepper.

Pour ¼ cup of heavy cream into the greased baking dish, sprinkle in ½ ounce of grated Parmesan and add the minced garlic.

Layer sweet potato slices, followed by parsnips and beet slices, repeating the process until all vegetables are used.

Season the top layer with salt and pepper, add the remaining grated Parmesan, cover with aluminum foil, and bake for 30 minutes.

Remove the foil, add the shredded Gruyère cheese and bake uncovered for another 18-20 minutes until melted and golden.

Garnish with additional fresh thyme leaves before serving.