In a small saucepan combine the sugar and the water and make the simple syrup by boiling them down together.
In a blender combine the raspberries and the chilled syrup and whizz on high. Run the mixture through a very fine mesh sieve to get rid of all the seeds. Return the sieved mixture back into the blender, add 15 medium sized basil leaves and whizz on high again. Transfer into a clean jug and cool in the refrigerator overnight.
Freeze the sorbet in the ice cream machine according to the manufacturer's instructions. Keep in an airtight container in the freezer or scoop right away.