Make the kaffir lime syrup by placing all ingredients for it in a small saucepan on medium heat. Bring it to boil. Remove from heat and strain into a small glass jar. Cool completely. Cover and store in the fridge until ready to use. Will keep in the fridge for up to 10 days.
Place half cup ice cubes in a cocktail shaker. Add gin,lime juice, kaffir lime syrup and matcha. Cover and shake for a couple of minutes until blended and chilled.
Add 5-6 ice cubes in a 230ml cocktail glass. Strain the cocktail over the ice in the glass. Garnish with a lime wheel and kaffir lime leaf. Serve immediately.