Preheat the oven to 375℉. Lightly grease a 9-inch baking dish with butter or nonstick baking spray. Set aside.

Using a mandoline, carefully slice the sweet potatoes horizontally into thin rounds, no larger than 1/8” thick. Place the sweet potato slices in a single layer in an overlapping pattern in the baking dish.

Set aside 1/2 cup of Gruyére cheese. Sprinkle the sweet potatoes with a third of the remaining Gruyére, cheddar, and Parmesan cheeses. Repeat with two more layers of potatoes and cheese.

Heat the olive oil in a medium saucepan over medium heat until shimmering. Add the garlic and cook, stirring occasionally, until golden and fragrant, about 5 minutes.

Add the cream, nutmeg, and thyme, and bring to a simmer. Cook, stirring often, until slightly thickened, about 5 minutes. Season with salt and pepper, to taste. Do not let come to a boil.

Stir in the reserved 1/2 cup of Gruyére cheese until melted. Slowly pour the warm cream mixture over the sweet potatoes, letting it sink in amongst the layers. Top with a bit of fresh thyme leaves.

Bake until the gratin is golden brown and bubbly and the potatoes are tender, about 45-50 minutes. If the gratin begins to brown too quickly, cover loosely with aluminum foil, as needed.

Remove from the oven and let rest for 10-15 minutes before serving. Garnish with more fresh thyme.