Combine both sugars and water in a saucepan over medium heat. Bring just to a boil, stirring until all sugar is dissolved.

Reduce heat to medium-low and add pumpkin, pumpkin pie spice, and cinnamon sticks. Simmer for 5 minutes, stirring until fully incorporated.

Remove from heat and strain through a mesh sieve or cheese cloth. Discard cinnamon sticks and transfer syrup to glass bottles. Store in the refrigerator for up to 2 weeks.

Strained pumpkin may also be saved for up to 2 weeks in an airtight container in the refrigerator.