Brew a shot of espresso using your Nespresso machine. If you're using a pod machine, insert a Nespresso pod and press the button to dispense a shot of espresso. If you're using a manual espresso machine, grind your beans and tamp them into the portafilter, then attach the portafilter to the machine and pull a shot.
Fill a cocktail shaker halfway with ice. Add the vodka, Kahlua, and freshly brewed espresso to the shaker.
If you like your martinis a little sweeter, you can add a splash of sugar or simple syrup to the shaker. To make simple syrup, combine equal parts water and sugar in a saucepan and heat over medium heat until the sugar is dissolved. Cool before using.
Shake the cocktail shaker vigorously for about 20 seconds, until the ingredients are well combined and the shaker is cold to the touch.
Strain the cocktail into a chilled martini glass.
Garnish the martini with a twist of lemon or orange peel, if desired.
Savor the flavors of the best Nespresso martini!