For the Crust

1. Preheat the oven to 325°F degrees and set a rack in the lower middle position. Wrap a 9- or 10-inch springform pan with with one large piece of heavy-duty aluminum foil, covering the underside and extending all the way to the top so there are no seams on the bottom or sides of the pan. Repeat with another sheet of foil for insurance. Spray the inside of the pan with nonstick cooking spray. Pulse the gingersnaps, sugar, and melted butter in a food processor fitted with the metal blade until finely ground. Transfer the moistened crumbs into the prepared pan and 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. Set a kettle of water to boil (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, 1-1/2 to 1-3/4 hours. A properly cooked cheesecake will jiggle a bit when you nudge the pan, but if the center seems at all liquidy, it's not done. CAREFULLY remove the roasting pan from the oven and set on a wire rack. Run a sharp paring knife around the edges 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 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, immediately stir in the hot cream a few tablespoons at a time. It will bubble up intensely, but it 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 14-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.
3. Freezer-Friendly Instructions: The cheesecake can be frozen for up to 3 months. To freeze: place the cake in the freezer briefly, unwrapped, to firm it up. Then double-wrap it tightly with aluminum foil or plastic freezer wrap, or place it in heavy-duty freezer bag. Thaw in the refrigerator the night before you plan to eat it.