To make the lychee juice: - peel and pit 6 - 8 lychee fruit over a medium sized bowl. Using a muddler (or a potato masher!) crush the fruit to extract the juice. Strain.
For the mint syrup: Combine ½ cup sugar and ½ cup water in a small saucepan. Bring to a simmer and cook until the sugar is dissolved. Remove pan from the heat and add ¼ cup fresh mint leaves. Stir and let infuse for approximately 30 minutes. Strain. Cover and refrigerate.
For the Lychee Cosmopolitan: Add the vodka, lychee juice, simple syrup and bitters to a cocktail shaker. Add 6 large ice cubes. Cover and shake for 45 seconds - until the shaker is frosted over. Remove the cap and strain into a small cocktail glass.
Notes
The mint simple syrup can be made a week or more ahead of time. To extend it's life, you can add ¼ oz. vodka to the syrup - or you can freeze it as well.