Preheat oven to 450°F with racks in top and lower third positions.
Whisk 2 tablespoons oil, 1 tablespoon thyme, the grated garlic and 1 teaspoon nutmeg in a large bowl.
Add sweet potato rounds and toss to coat.
Divide between 2 large rimmed baking sheets, spacing 1 inch apart.
Roast, rotating the pans between top and bottom racks and flipping the sweet potatoes halfway through, until tender, about 25 minutes. Transfer to a plate.
Brush the baking sheets with the remaining 1½ teaspoons oil.
Sprinkle ½ cup Parmesan in an even layer across the pans.
Arrange the sweet potatoes on top of the cheese.
Cover with parchment paper; use the bottom of a small bowl to press each round to ¼-inch thickness.
Remove the parchment and sprinkle the sweet potatoes with the remaining ½ cup Parmesan.
Roast, rotating the pans top to bottom halfway through, until browned and crisp, about 12 minutes.
Let stand for 2 minutes.
Use a thin spatula to transfer to a platter.
Let rest for another 2 to 3 minutes.
Garnish with thyme and/or flaky salt, if desired.
