Step 1: Set up your smoker according to the manufacturer’s directions and heat to 275 degrees. (Alternatively, you can grill the fruit on charcoal or gas grill.) Brush or scrape the grate clean and oil it well. Add wood chips or chunks (preferably fruitwood) to the fire, following the manufacturer’s instructions.

Step 2: Dip each nectarine half on all sides in the sugar. Smoke, turning with tongs, until caramelized (dark brown) on all sides, about 20 minutes. (2 to 4 minutes if direct grilling.)

Step 3: Transfer the nectarine halves to a plate to cool. Puree 3 halves in a food processor or blender. Cut the remaining half into thin wedges for garnishing the Bellini. Impale on cinnamon sticks, if desired.

Step 4: Add 2 tablespoons of puree to each of 4 champagne flutes. Fill each flute with chilled Prosecco and gently stir with the cinnamon stick or a bamboo skewer. Serve immediately.