Combine the basil leaves, gin, blueberry simple syrup, lemon juice, and egg white in a cocktail shaker without ice. Shake vigorously for at least 20-30 seconds.*
Add ice to the cocktail shaker and shake for another 20-30 seconds until very chilled.
Strain into a chilled coupe glass** and garnish with a fresh basil leaf and/or lemon slice.
Notes
*This technique is known as a "dry shake" (without ice.) It allows the egg white to mix into the other ingredients without being broken down with ice, and creates a frothy, creamy texture in the cocktail!**Any short glass will work if you do not have a coupe glass. I recommend popping it in the freezer for 4-5 minutes to chill it before serving. Alternatively, you can fill it with ice before straining the cocktail into it!