Preheat oven to 425°F. Fill a large bowl with ice water.

Bring a large saucepan of water to a boil. Add Brussels sprouts, reduce heat to maintain a lively simmer and cook until just tender when pierced with a paring knife, about 8 minutes. Drain the sprouts and plunge them into the ice bath. Let stand until cool enough to handle, then transfer to a clean dish towel and pat dry.

Spread the sprouts on a large rimmed baking sheet. Flatten them with the bottom of a mason jar or sturdy glass. Drizzle with oil and sprinkle with salt and pepper. Gently toss to coat. Sprinkle Parmesan evenly over the sprouts. Roast until the Parmesan has melted and started to brown, 5 to 7 minutes. Remove from oven and drizzle with vinegar.