Make the pumpkin butter by combining all the ingredients in a small saucepan. Bring to a simmer over low heat and cook for 5 minutes. Remove from the heat and allow to cool completely. Store in an airtight container in the fridge until ready to use. Will last for 2 weeks in the fridge.
Make the pumpkin spice kentucky mule by combining the bourbon, pumpkin butter, lemon juice and bitter in a cocktail shaker with some ice. Put the lid on and shake vigorously for about 15 seconds. Strain into a copper mug filled with ice and top with ginger beer. Garnish with a cinnamon stick.