Shake the gin, lemon and lime juices, simple syrup, egg white and bitters with ice, strain and serve in highball glass with 2 ice cubes.
Fill with club soda. Garnish with an orange peel and 2 bendy straws.
*Ginger-infused gin: In a clear glass jar with an air-tight lid, combine 1/4 cup sliced ginger and 3 cups gin. Allow to sit for 2 weeks in a cool, dry place, then strain into a clean bottle. Store in the refrigerator for up to 2 weeks.