Chop the tomatoes and place in a bowl with all the other ingredients except the basil leaves. If you have time, leave them to macerate at room temperature overnight. Blitz in a blender - in batches, then strain through a fine sieve. Shred the basil leaves and stir through.
Clear a shelf in the freezer and place a sided metal tray in to chill. Make up your mix and leave to cool, then pour into the tray and cover with cling film. Freeze the liquid until frozen around the edges and slushy in the middle. Use a fork to break up the ice into smaller crystals. Return the tray to the freezer.
Repeat the breaking up process every half hour (at least three times) until it’s completely frozen and the texture of snow. For a quicker method: freeze the mixture in an ice tray, then blitz the cubes in a food processor just before serving. The texture will be slightly slushier, but just as delicious.