Combine the sugar and the water in a large mason jar and stir until the sugar is dissolved.
Add the strawberries and the basil leaves to the jar and screw on the lid. Give the jar a gentle shake and place in the refrigerator for at least 12 hours or up to 2 days.
Strain the syrup through a fine mesh strainer. Store the syrup in the refrigerator for up to 2 weeks. Tip: Add an ounce of vodka or grain alcohol to help the syrup keep a bit longer.
For the cocktail:
Combine the gin, lemon juice, syrup, and aquafaba (or egg white) in a cocktail shaker.
Shake the cocktail without ice for 15-30 seconds to build the foam.
Fill the shaker 3/4 with ice and shake until chilled, about 12 seconds.
Strain the cocktail into a coupe glass and garnish with half a strawberry and a basil leaf.