Bake the pumpkin until it is soft and manageable then puree it with the cinnamon and nutmeg to taste. Puree the dark rum and caramel syrup together over ice and add the pumpkin puree. Shake and serve with a cinnamon stick for a garnish.
Place a tall-sided medium pot over a medium to medium-high heat. Slowly add the sugar, stirring and adding more sugar as it dissolves into a light brown caramel. Once all the sugar is added remove form heat and slowly add the water. You might have to return it to a medium heat to dissolve any chunks. Once the water is in add the cayenne and stir. Once everything is dissolved remove from heat and allow the syrup to cool. Transfer to a bottle. It makes about 2 1/2 cups of syrup and keeps for up to 6 months. Warning: The caramel will sputter when the water is added so be very careful not to get burned.
Series: Kitchen Conspirators Episode: Fall Harvest Cocktail (Ep. 3: Part 4)