Preheat your oven to 350°F (175°C). Grease the 9-inch springform pan and wrap the outside with two layers of heavy-duty aluminum foil.
In a mixing bowl, combine the graham cracker crumbs, ¼ cup of sugar, and the melted butter. Press the mixture evenly into the bottom of the springform pan, forming a firm crust. Use the bottom of a measuring cup to press down firmly.
Place the pan on a baking sheet and bake for 10 minutes. Remove from the oven and set aside to cool while you prepare the filling.
In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add the 1 cup of sugar and beat until well combined. Add the pumpkin puree, eggs (one at a time), vanilla extract, cinnamon, nutmeg, ginger, cloves, and salt. Mix until smooth and creamy.
Pour the cheesecake filling over the cooled crust in the springform pan.
Place the springform pan (still on the baking sheet) in the preheated oven. Bake for 60-70 minutes, or until the edges are set but the center is slightly jiggly. It will continue to set as it cools.
Remove the cheesecake from the oven and let it cool in the pan on a cooling rack for 1 hour. After 1 hour, refrigerate the cheesecake (still in the pan) for at least 4 hours, but preferably overnight.
Once chilled, remove the sides of the springform pan carefully. Slice and serve with optional toppings like whipped cream, pecans, or caramel sauce.