Add the granulated sugar, brown sugar, water, pumpkin purée, cinnamon, ginger, nutmeg, cloves, and salt to a medium saucepan. Whisk until everything is evenly combined.
Place the saucepan over medium heat and cook, stirring frequently, until the sugars dissolve and the mixture becomes smooth.
Reduce the heat to low and cook for another 5–7 minutes, stirring occasionally. Keep the mixture at a gentle simmer rather than allowing it to boil rapidly.
Remove the saucepan from the heat and stir in the vanilla extract. Let the syrup cool for several minutes so the flavors can settle.
Pour the mixture through a fine-mesh strainer into a clean heatproof jar or bottle. Press gently with a spoon to extract the liquid, if needed.
Allow the syrup to cool completely, then seal the container and refrigerate. The syrup can be kept refrigerated for up to 2 weeks and shake the syrup well before using and add 1–2 tablespoons to coffee, espresso, steamed milk, or other drinks. Adjust the amount to taste.