Preheat your oven to 350 degrees. Grease the bottom and sides of your springform pan using butter or cooking spray. Wrap the outside of your springform pan in heavy-duty tinfoil. The foil will keep the water from seeping in during the water bath.
Begin preparing your crust. In a medium bowl, mix the graham cracker crumbs, melted butter, and sugar. Use the crumb mixture to make a crust in the bottom of the springform pan. Press the crumbs firmly onto the bottom and sides of the pan. Bake the crust in the preheated oven for 5 minutes. Then set it aside.
Using a stand mixer (use the paddle attachment) or hand mixer, combine the softened cream cheese, remaining sugar, and vanilla. Beat until smooth. Next, add the pumpkin, eggs, cinnamon, ginger, nutmeg, and allspice. Beat on medium-low speed and mix the ingredients thoroughly. Take care to avoid overbeating, since that will cause cracking in your cheesecake. Stop mixing as soon as the batter is smooth and creamy. Pour the filling into the springform pan over the prepared crust.
Prepare a water bath. A water bath will produce hot-water steam in the oven, which will support a more even bake as well as prevent cracking on the top of the cheesecake. Place the springform pan in a large roasting pan. Put the two pans into the oven. Once they are both in the oven, carefully pour water into the roasting pan until an inch of water encompasses the springform pan.
Bake for 65 minutes. Avoid opening the oven door during baking, since this will change the temperature and cause cracks and sinking. The cheesecake should be firm around the sides and still somewhat jiggly in the center when it's done baking.
Turn your oven off, but keep your cheesecake in the oven, allowing it to come to room temperature. Prop open the oven door to let the steam escape. Once the cheesecake has cooled down, carefully remove it from the oven and the water bath. Wrap your springform pan in plastic wrap and place it in the refrigerator until the cheesecake is chilled, allowing the cake to firm up before slicing.
Once the cheesecake is chilled, remove the sides of the springform pan. Slice, serve, and enjoy!
Drizzle your pumpkin cheesecake with a sweet decadent caramel sauce, or add a simple dollop of whipped cream.