For the Crust

1. Preheat the oven to 325 degrees. Wrap a 9-inch springform pan twice with aluminum foil (preferably heavy duty). Take care to pull the foil all the way up the sides so that water cannot seep in from the water bath. Spray the bottom and sides of the pan with nonstick cooking spray. Pulse the crackers (or crumbs) and sugar in a food processor fitted with the metal blade until finely ground. Add the butter and pulse a few times to combine. Dump the moistened crumbs into the prepared pan and, using a measuring cup or glass, press into an even layer. Bake until fragrant and set, about 15 minutes. Cool on a wire rack while you prepare the filling.

For the Filling

1. Bring about 4 quarts of water to a simmer in a tea kettle (this will be used for the water bath). In a small, heavy saucepan, stir together the pumpkin, sugar, cinnamon, ginger, nutmeg, cloves and salt. Over medium heat, bring the mixture to a sputter, stirring constantly. Reduce the heat to medium-low and cook, stirring constantly, for 5 minutes, until thick, bronzed and shiny. Scrape the mixture into a large food processor fitted with the metal blade and process for 1 minute with the feed tube open.
2. With the motor running, add the cold cream. Add the cream cheese (cut into chunks) and process for about 30 seconds, scraping the sides if necessary, or until smoothly incorporated. Add the eggs and process for about 5 seconds or just until incorporated (do not overmix!).
3. Set the cake pan in a large roasting pan. Pour the batter into the cooled crust, and then pour enough boiling water into the large roasting pan to come about halfway up side of the cake pan. Bake until the cake is just set, about 1-1/2 hours. If it jiggles, it’s not done. CAREFULLY remove the roasting pan from the oven and set on a wire rack. Use a paring knife to loosen the cake from the sides of the pan. Cool until the water is just warm, about 45 minutes. Remove the springform pan from the water bath, discard the foil and set on a wire rack. Continue to cool at room temperature until barely warm, about 3 hours. Cover with plastic wrap and refrigerate until chilled, at least 4 hours or overnight.

For the Caramel Sauce

1. Stir the sugar, corn syrup, water and lemon juice together in a 2-cup microwave-safe measuring cup or medium glass bowl. Microwave until the caramel is pale yellow, or just barely starting to take on some color, 4-8 minutes (depending on the strength of your microwave). It’s fine to stop and open the microwave to check often; just don’t let it get too dark or it will burn. Let the caramel sit for about 5 minutes — it will gradually turn a rich amber color. (If after five minutes, it’s not dark enough, place it back in the microwave for thirty seconds or so, then let it darken again. If it gets too dark, start over.)
2. In the meantime, heat the cream in the microwave until hot. Once the caramel reaches the right color, add the hot cream a few tablespoons at a time. It will bubble up intensely, but won’t overflow. After you’ve added all the cream, stir to incorporate then add the butter. Add more cream if the mixture seems too thick. Once the caramel cools, you can store it in your fridge.

For Serving

1. Remove the outer ring from the springform pan. Slide a thin metal spatula between the crust and pan bottom to loosen, then slide the cheesecake onto a serving platter. (Alternatively, you can keep it on the pan bottom.) If there is condensation on the top of the cheesecake, blot it gently with a flat paper towel. Let the cheesecake stand at room temperature for about 30 minutes, then cut it into wedges. Warm up the caramel sauce in the microwave (it stiffens in the fridge). If it’s too thick, add more heavy cream to thin it out. Drizzle the caramel sauce over each piece of cheesecake and top with a dollop of sweetened whipped cream if desired.
2. Note: You’ll need a large food processor — preferably with a 12-cup capacity — to make the filling (you can also use an 11-cup, but you may have a bit of leakage). If you don’t have one, it’s fine to use a Kitchenaid Mixer or electric beaters for the filling and a small food processor for the crust.