Combine the gin, roughly chopped cucumber pieces, mint leaves, lime juice, honey, and ice in a blender. Blend on high for 30-60 seconds or until it resembles a slushy.
Pour the cocktails into two glasses and fill the rest of each glass with sparkling water and/or ice. Stir well, serve and enjoy!
The drink will separate, so serve it with a straw, so that you can stir it as needed while drinking.
If you don't like pulp in your drinks, strain the cocktail through a fine mesh sieve before drinking. The drink will be less likely to separate if you do this.
If you want to double or triple the recipe to make a pitcher of cocktails in advance, combine all of the ingredients except the gin and sparkling water in the blender. Strain through a sieve into a pitcher, cover and store in the fridge for a few hours. Add the gin and sparkling water just before serving, and stir well.