Put basil leaves in a large bowl or bucket and cover with water. Allow to rest for about 15 minutes, then drain in the colander and rinse again.
Process in batches, about 3 packed cups of basil at a time. Drizzle about 2 tablespoons of olive oil over the basil while processing. If it seems dry, add 1 tablespoon.
Transfer processed basil to the ice cube trays, pressing the chopped leaves down. Freeze until solid, about 8 hours, then remove and put in the large plastic freezer bag. Will keep for up to 6 months.