Add maple syrup, water, and pumpkin pureé to a small saucepan and whisk together over medium-high heat.
Using a small paring knife, carefully cut a slit in the vanilla bean from the top to the bottom. Using the edge of the knife, scrape the seeds from the vanilla bean pod.
Add cinnamon sticks, ginger, vanilla bean seeds (as well as the leftover pod) and cloves to the saucepan. Bring the mixture to a boil, then reduce heat slightly and simmer for 5-7 minutes.
Remove from heat and let the mixture sit for 15-30 minutes. Remove the cinnamon sticks with tongs, then strain the simple syrup through a fine mesh sieve.