Burrata cheese, a buttery-tasting blend of mozzarella and cream, is available at Italian markets, cheese shops, and some supermarkets.
Preheat oven to 400 degrees. Place grapes and rosemary on a rimmed baking sheet and drizzle with oil; sprinkle with salt and sugar. Roast until grapes are sizzling along the bottom and a few but not all have burst, 20 to 25 minutes. Smear cheese on crostini, and top with grapes.