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

Using a mandoline, slice the sweet potatoes, parsnips, and beets into thin rounds.

In separate bowls, mix sweet potatoes and parsnips with cream, half of the Parmesan, and thyme. Mix beet slices with the remaining cream, Parmesan, salt, and pepper.

Pour ¼ cup of heavy cream into the baking dish, sprinkle with the remaining Parmesan and add minced garlic.

Layer the sliced vegetables in the dish, alternating between sweet potatoes, parsnips, and beets.

Season the top layer with salt and pepper, sprinkle remaining Parmesan, and cover tightly with foil. Bake for 30 minutes.

Remove the foil and add shredded Gruyère cheese on top. Bake uncovered for an additional 18-20 minutes, until golden brown.

Let cool slightly, then garnish with fresh thyme before serving.