In medium saucepan, combine blueberries, sugar, lemon juice, mint, a pinch of salt, and 1/3 cup water. Bring mixture to a boil, then lower heat to low and simmer, stirring occasionally, for about 10 minutes

Carefully transfer to blender or food processor and puree. Using fine-mesh sieve over bowl, strain mixture and then discard solids. Let mixture cool; stir in kombucha.

Pour mixture into shallow 9 x 12 inch baking dish or another shallow container and place in freezer. Every hour, use tines of a fork to scrape ice crystals that form into center of dish, crushing any lumps. Don’t let mixture freeze solid. Repeat this step until all liquid has frozen into small crystals that resemble shaved ice, about 4 times total. Cover granita and keep frozen.

When ready to serve, scoop granita into serving bowls or glasses