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

Thinly slice the sweet potatoes, parsnips, and beets into very thin rounds using a sharp knife or a mandoline.

In each bowl, pour the designated amount of cream over the sweet potatoes and parsnips, adding 4 tablespoons in total, while drizzling 2 tablespoons over the beets. Add Parmesan and thyme and season with salt and pepper.

Pour ¼ cup of cream into the bottom of the baking dish, sprinkle with ½ ounce of Parmesan cheese and add the minced garlic.

Arrange the slices of sweet potatoes, parsnips, and beets in diagonal layers in the dish, seasoning generously with salt and pepper and adding remaining Parmesan on top.

Cover the dish tightly with aluminum foil and bake for 30 minutes or until tender.

Remove the foil and sprinkle shredded gruyère cheese over the top, baking uncovered for an additional 18 to 20 minutes until golden brown.

Allow to cool slightly, garnish with fresh thyme, and serve warm.