In a small saucepan, combine the water and erythritol sweetener. Simmer on medium low, stirring constantly, until erythritol dissolves. This will take about 5 minutes.
Turn the heat down to low and add the pumpkin pie spice and pumpkin puree. Mix and let sit for five minutes.
Take off the heat and strain the mixture through a mesh strainer. I find that using a ladle and discarding pulp after each ladleful is the easiest way to strain.
Cool to room temperature and then stir in the vanilla extract. The best way to enjoy this syrup is at room temperature for one month. You can prolong the life of the syrup by storing it in the refrigerator, but the mixture may crystalize because of the properties of erythritol.