Preheat the oven to 325°F (160°C). In a mixing bowl, combine crushed gingersnap cookies, granulated sugar, and melted butter until it resembles wet sand. Press into the bottom of a 9-inch springform pan. Bake for 10 minutes, then remove and cool completely.

In a large mixing bowl, beat softened cream cheese with an electric mixer on medium speed until smooth. Gradually add granulated sugar and vanilla extract, mixing until combined. Add eggs one at a time, mixing on low speed until incorporated.

In a separate bowl, combine pumpkin puree, cinnamon, nutmeg, and cloves, stirring until well mixed. Set aside.

Pour ¾ of the cheesecake batter into the cooled crust. Spoon the pumpkin mixture over it, creating swirls. Add dollops of the remaining batter and gently swirl with a knife.

Wrap the springform pan in aluminum foil and place it in a roasting pan. Fill the pan with hot water up to halfway up the sides of the cheesecake pan. Bake for 55-65 minutes, until edges are set.

After baking, turn off the oven and crack the door open to let the cake cool gradually. Let it rest in the oven for one hour, then refrigerate for at least 4 hours or overnight.