In a medium saucepan, combine the water, brown sugar, and granulated sugar. Place on medium heat and stir occasionally until the sugar dissolves.
1/2 cup granulated sugar, 1 cup water, 3 tbsp dark brown sugar
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!
Notes
Starbucks builds their Pumpkin Spice Latte with a sauce, not a syrup, and that sauce contains condensed skim milk. This version leaves the dairy out entirely, so it is vegan as written and it stirs into iced coffee and cold brew without changing the texture of the drink. It is also the safer one to make, since there is no condensed milk in the pan that can split on you. Strain it well. That single step is the difference between a syrup that pours clean and one that settles gritty at the bottom of the jar.