Combine the orange juice, grapefruit juice, and basil in a blender and process until smooth.
Pour into a 13x9" baking dish along with the kombucha and freeze for 30 minutes.
Use a fork to scrape apart any solid pieces that have formed, then return to the freezer for 30 minutes. Repeat 2-3 more times, until you have a crumbly, icy texture.