How to Make It
In a small bowl, dissolve the sugar in the hot water. Press the grated ginger through a fine strainer set over the bowl, releasing the juice.
In a cocktail shaker, muddle the diced cucumber with the 2 torn basil leaves. Add the ginger syrup, gin, lime juice and a handful of ice. Shake well, then strain into a martini glass. Garnish the martini with the cucumber slice and the remaining whole basil leaf and serve.