In a small saucepan or microwave-safe bowl, heat the sugar and water until the sugar dissolves and the mixture is clear. Pour into a glass or other container (to speed up the cooling process) and put into the fridge until it's cooled down.

Put the cucumber, mint and gin in the bowl of a food processor. Add the simple syrup and pulse until as well blended as you can get it. Scrape into the bowl of an ice cream machine and freeze according to the manufacturer's directions. (Alternatively, pour into a large loaf pan and freeze, stirring every hour or so until it's frozen.)