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

Slice sweet potatoes, parsnips, and beets into thin, uniform rounds using a mandoline slicer.

In each bowl, combine the sliced vegetables with heavy cream, grated Parmesan, minced thyme, and season with salt and pepper.

Pour any remaining cream, the rest of the Parmesan, and minced garlic into the bottom of the greased baking dish.

Layer the vegetables in the baking dish starting with sweet potatoes, followed by parsnips and beets, repeating until all are used.

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

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

Garnish with fresh thyme leaves before serving.