Fill an ice-filled cocktail shaker halfway with ice cubes.
Pour Baileys Coffee Irish Cream Liqueur, Smirnoff No. 21 Vodka, chocolate syrup, and a shot of espresso into a shaker with a peg measure.
Shake the cocktail shaker aggressively until the surface feels cool.
Pour the liquor into a martini glass using a cocktail strainer.
Using a grater, shred chocolate bits on top of the drink to make chocolate curls to garnish.