To make the cucumber syrup combine the sugar and water in a saucepan, and heat gently whilst stirring regularly until all sugar has dissolved. Then add in cucumber slices and leave them till the syrup cools completely. Discard the cucumber.
Make the Cucumber Matcha Cocktail:
Add the matcha into a good sized bowl and slowly add 2 tbsp of water, a little bit at a time, mixing constantly to make a smooth matcha paste. Then slowly mix in the rest of the water, followed by the gin, lime juice and cucumber syrup.
Place some cucumber slices and mint leaves in each cocktail jar and mash with a wooden spoon. Then add in some lime slices and ice before topping up with the cucumber matcha cocktail.