Place a coupe or martini glass in the freezer to chill while you prepare the drink.
Fill a cocktail shaker with ice (about 1.5 cups). Brew espresso and let it cool 3–5 minutes until warm, then add vodka, coffee liqueur, simple syrup, and the espresso to the shaker.
Seal and shake vigorously until well-chilled and very foamy, 15–20 seconds; the shaker should feel icy cold.
Double-strain into the chilled glass, allowing a creamy head of foam to settle on top.