Prepare the lime granita by combining the sugar with the water in a medium saucepan. Bring to the boil over a medium-high heat and then reduce to a simmer for 5 minutes. Remove from the heat and chill for 60 minutes.
After chilling, stir in the lime zest and lime juice. Pour the mixture into a shallow plastic tub and freeze.
Every 30 minutes, stir and break up the ice that forms with a fork and return to the freezer between times. Do so for 3 hours until you have a slushy, granular texture.
Before serving, prepare the brandy snap biscuits by melting together the sugar, syrup and butter. Allow to cool a little before stirring in the rest of the ingredients until smooth.
Pre-heat the oven to 180°C and grease and line a baking tray.
Drop tablespoons of the mixture onto the tray in discs, spaced apart and bake in the oven in batches if necessary for 6-8 minutes until just set. Remove from the oven and allow to cool on the tray a little before transferring to a wire rack to cool completely.
Transfer to an airtight container and serve with the lime granita at serving point. Garnish the granita with a lime wedge before serving.