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A couple of days before eating, tip everything into a blender or smoothie maker with 200ml water and blitz until very smooth. Pour into a freezable container and freeze overnight until solid.
A few hours before serving, remove from the freezer and allow to defrost slightly so it slides out of the container in a block. Chop the block into ice cube-sized chunks and blitz in the blender or smoothie maker again until you have a thick, slushy purée. Tip back into the container and refreeze for 1 hr or until it can be scooped out.
To serve, scoop the sorbet into chilled bowls or glasses and top with extra basil. If you want you can drizzle with something a little more potent, such as vodka or white rum.