Combine the brown sugar, water, ground cinnamon, ginger, cardamom, cloves, and vanilla in a small saucepan over medium heat. Bring to a boil. Once boiling, turn the heat down and allow to simmer for an additional 5-7 minutes, or until the sugar has dissolved and the mixture has started to thicken.
Pour your syrup into a storage container and cool to room temperature. Refrigerate and use within 2 weeks.
Fill a cocktail shaker cup with ice. Add your espresso shots, 1-3 teaspoons of the spice syrup (depending on how sweet you want your drink) and the pumpkin puree. Shake for 2 minutes.
Fill a glass with ice and pour the shaken espresso over the ice. Finish with a splash of oat milk and enjoy! Although not in the original recipe, you could add a dash of caramel sauce for an extra indulgent experience!