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

Slice the sweet potatoes, parsnips, and beets into very thin rounds and transfer each type to its own bowl.

Pour 4 tablespoons of heavy cream over the sweet potatoes and parsnips, and 2 tablespoons over the beets. Add Parmesan and thyme, season with salt and pepper, and toss gently.

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

Layer the vegetables starting with sweet potatoes, followed by parsnips and then beets, repeating until all vegetables are used. Top with remaining salt, pepper, and Parmesan.

Cover with aluminum foil and bake for 30 minutes or until the vegetables are tender.

Remove the foil, sprinkle shredded gruyère over the top, and bake uncovered for an additional 18-20 minutes until lightly browned.

Let it sit for a few minutes, then garnish with fresh thyme leaves and serve warm.