To make the simple syrup, add pumpkin puree, water, sugar and pumpkin pie spice to a small saucepan. Bring mixture to a boil over medium-high heat, stirring constantly.
Once the syrup is boiling and smooth, remove from heat and cover. Let sit for 15 minutes.
Strain the pumpkin mixture into an airtight container.
Let cool completely before making the cocktail.
Syrup can be stored in the refrigerator for up to 1 week.