Pick all the leaves from your basil. Place them in a food processor bowl. Process, scraping down as needed, until the basil is minced.
Drizzle in olive oil with the machine running, just until a paste is produced.
Scrape the paste into sturdy quart-sized zip-top freezer bags, and flatten into a sheet, about 1/3 inch thick. Label the bag and lay flat in the freezer until solid.
To use, break off a chunk of the paste and add to pestos, sauces, soups, or anything else that needs a little basil, and a little taste of Summer!