Puree kiwi and 2 ounces of simple syrup.
In a cocktail shaker combine kiwi mixture, lemon juice, gin and egg white (if using). Do not add ice.
Shake vigorously for at least 15 seconds.
Add ice to shaker and then shake again.
Strain into chilled, ice-filled rock glasses.
Squeeze a small bit of lemon juice over the top and then garnish with kiwi slices