Cut the cucumber into small chunks and drop into a blender. Top with the mint leaves, sugar and salt and add a little water to get things going. Puree the cucumber and mint until smooth. You may need to press down on the cucumbers to get them into the blades. Add a little more water if needed. Place a fine mesh strainer over a bowl and pour in the cucumber puree. Leave the puree to sit and drain into the bowl for about half an hour. You can shake the strainer, but don’t press down on the solids or the mixture will become cloudy and pulpy – and you don’t want your drink to become too thick as the ice melts. Pour the liquid into a 2-cup measuring cup (you should have about 1 cup of liquid). Add enough water to make two cups. Pour the cucumber juice into ice cube trays and freeze until solid. Don’t throw away the pulp from the cucumbers, it’s great stirred into Greek yogurt to make a dip for fresh vegetables.
Place three to four cucumber cubes into a double old fashioned glass and add the gin, pour over the tonic and add a mint sprig. Enjoy!