To make the syrup, dissolve the brown sugar into the water, add the cinnamon stick, and bring it to a brief boil. Add the vanilla and let the cinnamon stick steep while it cools (then discard the cinnamon stick). It will keep in the fridge for a few weeks.
To make your drink, make 3 "short" shots of espresso (on a Nespresso machine it's the left-hand smaller button).
Fill a shaker glass or large mason jar with ice, add 2-4 tablespoons of syrup (to taste...I tend toward 2 tablespoons) and the espresso.
Shake vigorously (original recipe says for 1 minute but I'm lazy, and 15 seconds yields great results).
In a glass add some ice and the milk you want. Strain the shaken mixture into your glass over the milk, making sure you keep some of the foam. Stir to combine, and enjoy!
Notes
Any espresso machine will work, I'm just partial to Nespresso because it's SO easy and produces amazing crema