Here is the basil syrup mentioned below.
1/4 cup sugar
3 cups fresh basil leaves
Heat sugar with 1/4 cup water in a small saucepan until sugar is dissolved. Transfer to blender.
Bring a saucepan of salted water to a boil. Submerge basil in it and boil for 3 minutes. Drain basil in a colander and run cold water over it to stop the cooking. Place basil in blender with syrup and process for 2 minutes. Strain in a sieve. Sprinkle with salt.
(I probably wouldn't add salt if I wanted to use this for cocktails.)