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

Slice the sweet potatoes, parsnips, and beets into thin rounds and place in separate bowls.

Toss the sweet potato and parsnip slices with 4 tablespoons of heavy cream, ½ ounce of grated Parmesan, and 1 teaspoon of minced thyme. For the beets, mix with 2 tablespoons of cream and ½ ounce of Parmesan, seasoning with salt and pepper.

Pour ¼ cup of heavy cream into the bottom of the baking dish and sprinkle with ½ ounce of Parmesan. Add minced garlic.

Layer the sweet potatoes, parsnips, and beets, continuing until all vegetables are used.

Season the top with salt and pepper and sprinkle the remaining Parmesan. Cover with aluminum foil and bake for 30 minutes.

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

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