Step 1: Preheat your oven to 325°F (165°C). Mix cookie crumbs and melted butter; press into the bottom of a 9-inch springform pan. Bake for 10 minutes, then cool.
Step 2: In a large bowl, beat the cream cheese and sugar until smooth and fluffy. Add eggs one at a time, followed by the vanilla, mixing on low just until combined.
Step 3: Divide the batter into two separate bowls. Into one bowl, fold in the pumpkin puree, cinnamon, ginger, and cloves.
Step 4: Into the second bowl, fold in the melted and cooled bittersweet chocolate until fully incorporated.
Step 5: Drop alternating spoonfuls of the pumpkin and chocolate batters into the prepared crust. Use a knife to gently swirl the batters together in a figure-eight motion.
Step 6: Place the pan in a water bath and bake for 65-75 minutes, or until the edges are set but the center still jiggles slightly.
Step 7: Turn off the oven and leave the cheesecake inside with the door cracked for 1 hour. Remove and cool completely on a wire rack before refrigerating for at least 6 hours.