Prepare the Crust:
Preheat your oven to 350°F (175°C). In a medium bowl, combine the crushed gingersnap cookies, chopped pecans, and melted butter. Press the mixture firmly and evenly into the bottom of a 9-inch springform pan. Bake for 10 minutes. Remove and let it cool completely on a wire rack.

Mix the Cheesecake Batter:
In a large bowl, use an electric mixer to beat the softened cream cheese until completely smooth and free of lumps. Gradually add ½ cup of the sugar, beating until well combined. Beat in the vanilla extract. Add the eggs one at a time on low speed, mixing just until incorporated after each addition. Be careful not to over-mix the batter.

Create the Pumpkin Mixture:
In a separate bowl, whisk together the pumpkin puree, the remaining ¼ cup of sugar, ground cinnamon, and ground nutmeg until smooth. Gently fold about one cup of the plain cheesecake batter into this pumpkin mixture to lighten it for swirling.

Layer and Swirl:
Pour the remaining plain cheesecake batter over the cooled crust and spread it into an even layer. Drop spoonfuls of the lightened pumpkin batter over the top. Use a butter knife or a skewer to gently drag it through the batters in a few figure-eight motions to create a beautiful marbled or swirl effect.

Bake the Cheesecake:
Bake for 50-60 minutes, or until the edges of the cheesecake are set and the center has only a slight jiggle. Turn the oven off and let the cheesecake cool inside with the oven door ajar for one hour. This gradual cooling process is key to preventing cracks.

Chill Completely:
Remove the cheesecake from the oven and allow it to cool to room temperature on a wire rack. Once cooled, cover it with plastic wrap and transfer it to the refrigerator to chill for at least 6 hours, or preferably overnight, for the best texture and flavor.