In a small saucepan, combine strawberries, basil, sugar, and water. Bring to a boil, reduce heat, and cook until strawberries have broken down, about 6-7 minutes.
Transfer strawberry mixture to food processor or blender and puree until smooth. Let cool completely.
Pour ⅓ of the puree into a large glass pitcher. Add about 5 cups of kombucha and stir with a plastic or wooden spoon. Using a plastic funnel, pour liquid into a 34-ounce swing top bottle (alternatively, you can use mason jars or other tightly sealed jars). Repeat with remaining two bottles.
Store bottles in a dark and cool place for 2-4 days, then transfer to fridge. Strain strawberry pulp before serving.