Make the hazelnut syrup: In a small saucepan, combine water and sugar over medium heat. Stir until sugar dissolves completely, about 2 minutes. Remove from heat and stir in hazelnut extract. Let cool while you prepare the espresso.
Brew 2 shots of espresso using your espresso machine or Moka pot. Pour the hot espresso into your serving mug.
Add 2 tablespoons of hazelnut syrup and vanilla extract to the hot espresso. Stir immediately to combine and release the aromatic oils.
Heat the milk in a small saucepan or microwave until steaming but not boiling, about 150°F. If you have a milk frother or steam wand, heat and froth simultaneously for 30-45 seconds until doubled in volume.
For manual frothing: Pour heated milk into a French press or mason jar. Pump the plunger vigorously for 30 seconds until thick foam forms on top.
Tilt your mug at a 45-degree angle and slowly pour the frothed milk down the side, allowing the foam to settle on top naturally.
Dust the foam lightly with cocoa powder if desired. Serve immediately while hot and enjoy within 5 minutes for the best texture.
