How to Make It
In a small saucepan, combine the water with the sugar. Bring to a simmer and cook over moderate heat until the sugar dissolves, about 1 minute. Transfer the sugar syrup to a small bowl and let stand until cool, about 20 minutes.
In a large pitcher, mix the coconut milk with the lime juice and sugar syrup. Pour in the vodka. Fill the pitcher with ice and stir until the mixture is chilled. Pour the mixture into martini glasses, sprinkle with the lime zest and serve.
Mango vodka is available commercially, but you can also make it at home: In a jar, combine 2 cups of vodka with 2 cups of diced fresh mango. Cover and refrigerate overnight or for up to 4 days. Strain, discarding the mango.