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

Thinly slice your sweet potatoes, parsnips, and beets. Transfer each type of vegetable into separate bowls.

Coat each bowl of sliced vegetables with heavy cream, grated Parmesan, minced thyme, salt, and pepper. Stir gently.

Pour 1/4 cup of heavy cream into the bottom of the greased baking dish. Sprinkle with minced garlic and a bit more grated Parmesan.

Arrange the coated vegetables in the baking dish, alternating between sweet potatoes, parsnips, and beets.

Cover the baking dish tightly with foil and bake for approximately 30 minutes.

Remove the foil and sprinkle the top liberally with shredded Gruyère cheese. Return to the oven for an additional 18-20 minutes.

Once the top is bubbling and golden, remove from the oven and garnish with fresh thyme leaves. Let sit before serving.