In a medium saucepan, combine the water, brown sugar, and granulated sugar. Place on medium heat and stir occasionally until the sugar dissolves.
Add in the cinnamon sticks, pumpkin puree, ground nutmeg, ground cloves, and ground ginger. Stir one more time to combine, and bring to a simmer. Reduce the heat and keep simmering the mixture for 15-20 minutes. The syrup will slightly thicken.
Strain the syrup into a mason jar, discard the solids, and use immediately or let it get to room temperature then store in the fridge for whenever you're ready to make your lattes!