In a small saucepan, combine the brown sugar, banana, cinnamon stick and 2/3 cup of water. Bring to a simmer and heat for 10-12 minutes, stirring and mashing the banana occasionally. Move the pan off the heat and stir in the vanilla. Strain the solids from the syrup, squeezing the balls off the banana to get as much liquid out as possible. Leftover syrup will keep in the fridge for up to a week.
In a shaker, combine the vodka, Kahlua, banana syrup, and espresso hots. Fill with ice and shake vigorously until cold. Strain into a coupe glass - notice how the crema separates and floats to the top!
Thread a few banana bread chunks onto a skewer and set atop your coupe glass. Arrange three little coffee beans in the classic espresso martini triangle arrangement.