Add Midori, gin, lemon juice, simple syrup, and egg white to a shaker. Dry shake (no ice) until frothy.
Add ice and shake vigorously again until well chilled and extra frothy.
Strain into a chilled glass.
Garnish with a lemon wheel or cherry.
Notes
Use aquafaba for a vegan-friendly version. For a classic sour, reduce Midori and add more gin. Use pasteurized egg for safety, or skip for a lighter cocktail (won’t be as creamy).