Preheat the Oven

• Preheat your oven to 375°F (190°C). Grease a 9×13-inch baking dish with butter or nonstick spray.

Prepare the Cream Mixture

• In a medium saucepan over medium heat, combine the heavy cream, whole milk, minced garlic, thyme, salt, and pepper. Bring to a gentle simmer, then remove from heat.

Assemble the Gratin

• Arrange a layer of sweet potatoes in the bottom of the prepared baking dish. Follow with a layer of Yukon Gold potatoes, then parsnips, and turnips.
• Sprinkle each layer lightly with Gruyère cheese as you assemble. Repeat the layers until all vegetables are used.

Add the Cream Mixture

• Pour the warm cream mixture evenly over the layered vegetables, ensuring it seeps through to the bottom.

Add the Topping

• Sprinkle the top of the gratin with the remaining Gruyère and Parmesan cheese.

Bake the Gratin

• Cover the dish with aluminum foil and bake in the preheated oven for 45 minutes.
• Remove the foil and bake for an additional 20-25 minutes, or until the top is golden brown and the vegetables are tender when pierced with a fork.

Rest and Serve

• Let the gratin rest for 5-10 minutes before serving to allow the layers to set. Serve warm.