Combine the brandy, simple syrup, lemon juice, lime juice and egg white in a cocktail shaker. Cover and shake well until the mixture is frothy. Remove the lid, fill the shaker with ice, and then cover and shake vigorously again until very cold.
Strain into a 6-ounce footed highball or rocks glass. Drop 2 to 3 drops of the bitters onto the top of the foamy drink and use a toothpick to swirl the bitters into a yin/yang formation. Serve immediately.