Special equipment: a milk frother
Bring the milk to a simmer over low heat. Froth the milk using a milk frother or a whisk. Combine the espresso shots and a tablespoon of Pumpkin Spice Syrup in 2 large coffee mugs and stir half of the milk into each. Sprinkle the tops with spice, if desired. Drink immediately!
Combine the pumpkin puree and pumpkin pie spice in a small saucepan over medium heat and cook until the mixture thickens slightly and the spices become fragrant, about 3 minutes.
Combine 2 cups cold water and the granulated and brown sugars in a medium saucepan, bring to a boil over high heat and cook, whisking occasionally, until the mixture thickens and reduces slightly, about 5 minutes.
Reduce the heat to low, whisk in the spiced pumpkin puree and cook, stirring occasionally for 10 minutes. Do not allow the mixture to boil after you add the pumpkin or the syrup will become cloudy (even after straining.) Remove from the heat and let the mixture cool for 10 minutes.
Place a mesh strainer over a medium bowl and line the strainer with several layers of cheesecloth. Pour the mixture through the strainer and let it strain slowly into the bowl. Add the vanilla extract to the syrup and transfer to a container with a tight fitting lid. The syrup will last 1 month stored in the refrigerator. Makes about 1 1/2 cups; leftovers can be refrigerated for 1 week.