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

Slice the sweet potatoes, parsnips, and beets into very thin rounds (approx. 1/8 inch thick).

Mix sweet potato and parsnip slices with 4 tablespoons of heavy cream, 2 ounces of Parmesan, half of your minced thyme, salt, and pepper.

In another bowl, coat beet slices with 2 tablespoons of heavy cream, remaining Parmesan, other half of thyme, salt, and pepper.

Pour 1/4 cup of heavy cream into the baking dish and add half an ounce of Parmesan and minced garlic.

Layer the vegetables starting with sweet potatoes, followed by parsnips and then beets. Repeat until all are arranged.

Sprinkle with salt and pepper and distribute the remaining Parmesan cheese on top.

Cover with aluminum foil and bake for 30 minutes. Vegetables should be tender.

Uncover, sprinkle Gruyère cheese on top, and bake for an additional 18-20 minutes until golden brown.

Garnish with fresh thyme leaves and let the gratin rest before serving.