Make the rose cardamom syrup first: In a small saucepan, combine water, sugar, and crushed cardamom pods. Heat over medium heat, stirring until sugar dissolves completely, about 2 minutes.
Remove the saucepan from heat and let the cardamom steep for 5 minutes. Strain out the pods, then stir in rose water and vanilla extract. Set aside to cool slightly.
Brew two shots of espresso directly into your serving mug. Add 2 tablespoons of the rose cardamom syrup and stir to combine while the espresso is hot.
Heat the milk in a small saucepan or microwave until steaming, about 150-155°F. Use a milk frother or whisk vigorously for 30 seconds to create microfoam.
Pour the frothed milk over the espresso mixture, holding back the foam with a spoon. Spoon the remaining foam on top.
Garnish with a light sprinkle of ground cardamom or a few dried rose petals if desired. Serve immediately while hot.
