Brew your espresso shots using your preferred espresso making method into a cup. See my blog post on Five Ways to Make Espresso at Home. To a cup, combine the vanilla syrup and the espresso shots and stir to combine.
Add chocolate milk to a milk frothing pitcher and steam using a steam wand. If you don't have an espresso machine with a steam wand, you can warm and froth the milk using an aerroccino, or you could warm the milk in a pot/ in the microwave, and froth the warmed milk with a handheld milk frother until foamy.
Pour the steamed chocolate milk over the vanilla syrup-espresso mixture, top with whipped cream (optional), and enjoy!