Chop honeydew melon into cubes and place in a food processor. Process until smooth. Muddle cucumber and mint together in the bottom of a tumbler. Add gin, honeydew juice, lemon juice, simple syrup and a good handful of ice. Cover and shake for 10 seconds. Remove cover and set strainer on top of the tumbler. Holding a fine mesh sieve in your other hand over the glass, pour the drink through the sieve to strain. Serve up. Skewer a ribbon of cucumber for garnish.