In a pot, combine 1 cup sugar with 1 cup water and 10 basil leave. Bring the mixture to a rolling boil until the sugar is dissolved. Remove from heat and let the basil infuse for 20 minutes and until the mixture has cooled. Strain out the basil and set the simple syrup aside.
Peel a large English cucumber and cut it into chunks. Place it into your food processor and blender and pulse for 2 minutes. Remove mixture and place it into a fine mesh strainer and push out the juice into another bowl. Discard whatever cannot be pushed into the juice. Set aside.
In a cocktail shaker, combine 1 oz of basil simple syrup. 1 oz cucumber juice, 3 oz gin, 1 oz of lime juice and ice cubes. Shake shake shake and taste. If it's too strong, add 1 more oz of basil simple syrup. Shake again and serve over ice.