Best martini I ever had was a Lemongrass Martini, served at La Lucciola Restaurant, Bali, Indonesia. Don't have precise recipe but I watched the bartender make it. Ginger in Bali is very plump and fresh out of the ground and exudes quite a bit of juice when squeezed:

Into a martini shaker with crushed ice, add premium vodka of choice, squeeze the juice from a large piece of fresh Balinese ginger (using a squeeze juicer), take two reeds of lemongrass, tie in a knot, pull tightly so lemongrass oil drips into martini (from where the knot is in the lemongrass) shake, strain and pour into up martini glass, and insert the knoted lemongrass into the martini (straw like) as garnish. Fantastic!