To begin, brew your espresso (unless using cold brew concentrate).See Notes for how to brew
Place your serving glasses in the freezer to chill while you make the martinis or at least 5 minutes.
Add all of the ingredients to the cocktail shaker. (Vodka, kahlua, espresso, and simple syrup and about 1 cup of ice)See notes for how to make your own simple syrup
Seal the shaker tightly and shake for about 15-20 seconds until very well chilled.
Strain into your chilled espresso martini glasses then garnish with coffee beans.
Notes
To brew espresso in a moka pot: Add water to the bottom portion of the moka pot just up to the bottom of the valve. Add the coffee basket over the water and fill to the top with coffee grounds. Do not pack them tightly down but just press slightly to flatten grounds. Screw the top of the moka pot on very tightly. Place on the stove and heat over high heat. You will hear it bubbling up then it will slow and get quieter when finished. Allow it to cool then pour any left over coffee into an airtight container and store in the fridge for no more than 5 days. To make simple syrup:add 1 cup of water and 1 cup of sugar to a saucepan. heat over medium heat until the sugar is dissolved then allow to cool.