PREPARATION: Preheat oven to 325 degrees Fahrenheit. Place oven rack at center. Strain the pumpkin by spooning it into a paper towel-lined fine mesh colander and pressing out excess liquid by running a rubber spatula or large spoon across the pumpkin a time or two. Set aside.
CRUST: In a medium bowl, whisk together the graham cracker crumbs, 1/4 cup of the chopped pecans, sugar, ginger, cinnamon, allspice, salt, pepper, and cayenne pepper. Stir in melted butter until well-blended. Spoon into a 9-inch springform pan and press evenly across bottom and up at least ½-inch on the sides. Sprinkle the remaining 1/4 cup chopped pecans over the bottom of the crust. Refrigerate while you make the filling. (Can do this is the food processor, but be careful not to over-process as the nuts are easily chopped too finely.)
FILLING: In a food processor fitted with a S-blade or an electric mixer fitted with the flat beater, pulse or beat the cream cheese until smooth. Add the lemon juice, vanilla extract, almond extract, sugar, salt, cinnamon, ginger, cloves, and nutmeg and pulse or mix well. Spoon or scrape in the strained pumpkin and pulse or mix well. Add the eggs one at a time, mixing briefly after each addition. Stir in cream.
ADD FILLING TO CRUST AND BAKE: Place two large sheets of aluminum foil around the bottom and up the sides of the the springform pan and place it in a roasting pan. Pour the filling into the crust in the springform pan. Place roasting pan on the oven rack, fill with hot water half-way up the sides of the springform pan, and bake for 55-60 minutes or until the cake is at 150 degrees F (use an instant read thermometer) or firm with the exception of the center, which should still be a little jiggly. (A baking pan full of water is called a bain marie and ensures even baking.)
COOL/SERVE: Remove the roasting pan to a cooling rack. Holding the pan with an oven mitt or towel, carefully run a thin, small knife around the edges of the cake to loosen it. Let it sit in the water bath until water is barely warm—another hour. Take the cake out of the roasting pan, pour out the water, discard the foil or save for another use, and place just the springform pan back on the rack to cool completely: 2-3 hours. Cover with plastic wrap or foil and refrigerate for at least two hours or overnight. To serve, remove from the refrigerator and let rest 30-60 minutes before removing sides of the pan, cutting, and serving with Ginger Whipped Cream (see Notes), if you like. You can dip the knife into hot water, wipe it quickly on a towel, and then cut the cake for clean, neat slicing. You’ll need to repeat dipping in hot water and wiping for each cut.
STORAGE: Cheesecakes store well in the refrigerator, well-covered, for up to a week and covered with foil or in a freezer bag in the freezer for up to 3 months. If frozen, thaw overnight, wrapped, in the refrigerator before resting 30-60 minutes at room temperature and serving.