Preheat the oven to 425°F.
Position a rack in the center of the oven. Line a large rimmed baking sheet with parchment paper.
To a large bowl, add the olive oil, garlic, salt, pepper, and red pepper flakes (if using). Stir to combine.
Trim the tough stems off of each Brussels sprout and remove any shriveled or yellowing outer leaves. Cut each sprout in half lengthwise through the stem and core, adding to the olive oil mixture as you slice. Toss until coated.
Add 1 tablespoon of the Parmesan to the Brussels sprouts and toss to combine. Spread the remaining cheese in an even layer over the center of the prepared baking sheet.
Arrange the Brussels sprouts cut side down in a single layer on the cheese-laden area of the baking sheet.
Roast the Brussels sprouts until the cheese is melted, golden brown, and crisp, 14 to 17 minutes.
Use a thin spatula to transfer the Brussels sprouts along with the stuck-on crisp Parmesan to a serving platter and serve.
