Make the crust
Position a rack in the center of the oven and heat the oven to 350°F.
In a food processor, pulse the cookies and sugar until finely ground. Add the butter and pulse until evenly moistened. Using your fingers, press the crumb mixture into the base and partway up the sides of a 9-inch springform pan. Use a flat-bottomed, straight-sided glass to further press and smooth the bottom and nudge the crumbs halfway up the sides.
Bake until firm, 8 to 10 minutes. Transfer to a rack to cool. Position the oven rack in the bottom third of the oven and leave the oven on. When the pan is cool, wrap the bottom and sides with 2 overlapping 18-inch squares of heavy-duty aluminum foil and set in a large baking pan.
Fill and bake the cake
In a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed until smooth, about 1 minute. Add the sugar and beat until combined. Mix in the pumpkin, cinnamon, nutmeg, cloves, and vanilla until smooth. Mix in the eggs, egg yolk, and 1-1/4 cups of the cream just until well combined. Set aside.
Heat the remaining 1/3 cup cream in a small saucepan over medium heat to just below a boil; remove from the heat. Add the chocolate and let sit for 2 minutes. Whisk until smooth and then whisk in 1 cup of the pumpkin batter.
Pour the remaining pumpkin batter into the prepared crust. Drop 2-tablespoon dollops of the chocolate batter over the pumpkin batter. For the marbled look at right, work in one quadrant and use a wooden skewer or toothpick to continuously “write” capital cursive L’s, being careful not to go too deep and scrape the crust. Turn the pan to work in the next quadrant and continue swirling and turning until all quadrants are done. (For other patterns for swirled cakes, see "Marbling and Beyond.")
Pour 1 inch of boiling water into the baking pan. Bake until only the center of the cake jiggles when nudged, 1 hour 15 minutes to 1 hour 25 minutes. Turn the heat off but leave the cake in the oven with the door ajar for another 45 minutes.
Remove from the water bath and foil and run a thin, sharp knife around the edge of the cake. Cool completely on a rack. Cover the pan with plastic wrap (without letting it touch the cake) and chill for at least 8 and up to 24 hours.
Make the whipped cream and serve
Whip the heavy cream, sour cream, honey, and vanilla to medium-soft peaks.
Remove the side of the springform pan. Run a long, thin metal spatula under the bottom crust and carefully slide the cheesecake onto a flat serving plate. Use a knife warmed in hot water and wiped dry to cut the cake, wiping it clean and reheating it after every slice. Serve with the whipped cream.
nutrition information (per serving):
Photo: Kate Sears