Add the brown sugar to a shallow bowl. Moisten the rims of two chilled glasses with a sliced orange wedge and dip in the sugar mixture. Set aside.

Place the cider, cider syrup, gin, orange juice, egg white, and half-and-half/cream into a large shaker (without ice). Shake vigorously for about 1-2 minutes, then fill the shaker with ice. Continue to shake until everything is cold and frothy. Divide 1/4 cup of the club soda to the glasses. Strain the mixture into the glasses. Pour the remaining club soda into the shaker to pick up the foam left behind. Spoon the remaining fizz on top of the glasses and garnish each glass with a cinnamon stick and/or apple slices. Serve immediately.