Process 1/2 cup orange juice and basil leaves in a blender or food processor 10 seconds. Pour mixture through a fine wire-mesh strainer into a 4-cup glass measuring cup; add remaining 2 1/2 cups orange juice.
Divide mixture between 2 zip-top plastic freezer bags. Place bags on a jelly-roll pan. Freeze 6 hours or until firm. Remove bags from freezer, and let stand 10 minutes. Break mixture into small chunks using hands.
Process chunks, in batches, in a blender or food processor until smooth. Serve immediately. Garnish, if desired.