Preheat an oven to 425 F.
In the work bowl of a food processor fitted with the shredder attachment, shred the Brussels sprouts. Transfer to a rimmed baking sheet and toss with the olive oil. Season generously with salt and pepper. Roast until wilted and lightly browned, about 12 minutes. Remove from the oven and toss with the Parmigiano. Serve immediately.