Stir together sugar and water in a small saucepan. Bring to a simmer over low heat. Remove from heat and add cinnamon and rosemary. Cover and let steep 1 hour.
Discard cinnamon and rosemary. Spoon 1 1/2 tablespoons syrup into a small bowl and refrigerate until cold, about 10 minutes.
Put egg white, rum, and chilled syrup in a shaker. Cover and shake hard 15 seconds. Add ice to shaker and shake hard until chilled and frothy, 30 to 45 seconds.
Strain into 2 coupe glasses. Top each with 3 to 4 ounces wine. Garnish with a pinch of ground cinnamon and fresh rosemary. Serve immediately.
