First, blanch and shock the basil. This will keep the basil butter bright green and full of fresh flavor. Bring a small pot of water to a boil. Make an ice water bath in a medium bowl.
Add the basil leaves to the boiling water and cook until bright green and wilted, 20-30 seconds. Drain well and immediately plunge into the ice water bath to stop the cooking.
When the basil is cold, drain it well and squeeze it with your hands to remove as much liquid as possible. Chop the basil finely.
Place the softened butter in a medium bowl with the lemon zest and salt. Add the chopped basil and stir it into the butter.
If you like, beat the soft butter with a spatula or electric beaters to lighten it. Alternatively, place everything in the bowl of a small blender or food processor and pulse until lightly aerated, being careful not to melt the butter.
Swirl the butter into a serving bowl or storage container. Use right away or refrigerate until cold, 1 hour and up to several weeks. Or freeze for longer storage.
