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

Thinly slice sweet potatoes, parsnips, and beets into 1/8 inch rounds and place in separate bowls.

In a mixing bowl, combine sweet potato and parsnip slices with 4 tablespoons of heavy cream, 2 ounces of grated Parmesan, minced thyme, salt, and pepper. In another bowl, coat the beet slices with 2 tablespoons of heavy cream, the remaining 2 ounces of Parmesan, salt, and pepper.

Pour ¼ cup of heavy cream into the bottom of the greased baking dish and sprinkle with half an ounce of Parmesan and minced garlic. Layer sweet potato, parsnip, and beet slices alternately.

Sprinkle with remaining salt, pepper, and half an ounce of Parmesan before covering with aluminum foil and baking for 30 minutes.

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