In a medium saucepan, add the sugar and water. Heat over medium-heat, whisking occasionally, as it is brought to a boil. Remove from heat and cool to room temperature. Stir in vanilla extract. Store in a covered container, and keep refrigerated. You will be able to make about 10 vanilla lattes with this recipe for vanilla syrup.
MAKE THE VANILLA LATTE:
In a mug, combine hot espresso with vanilla syrup.
Heat the milk to steaming. Do this in a saucepan on the stovetop or in the microwave in a microwave-safe bowl.
Use a milk frother to froth the hot milk. If you don't have a milk frother, you can use an immersion blender, or put the steamed milk in a shaker bottle and shake vigorously.
Pour the steamed/frothed milk into the mug with the espresso and vanilla syrup; stir, using a spoon to hold back the milk froth. Spoon the milk froth on top; serve immediately.