Brew the coffee or espresso. Pour into a coffee mug.
Warm the milk in a small saucepan over medium heat until it steams and tiny bubbles form. Remove from heat and stir in the vanilla syrup.
Pour the milk into a tall glass. Using a handheld frother, froth the milk. (Alternatively, seal the milk in a mason jar with a lid and shake vigorously for 30 seconds.)