Preheat oven to 350°F (175°C).
In a medium bowl, combine gingersnap crumbs, pecans, and melted butter. Press into the bottom and up the sides of a 9-inch springform pan.
In a large bowl, beat cream cheese, 1/2 cup sugar, and vanilla until smooth. Add eggs one at a time, mixing well after each addition.
Set aside 1 cup of the cream cheese mixture. To the remaining batter, add 1/4 cup sugar, pumpkin puree, cinnamon, nutmeg, and allspice. Mix until well blended.
Spread the pumpkin batter into the crust, then spoon the reserved plain batter over the top and swirl with a knife to create a marbled effect.
Bake for 55 minutes or until the filling is set. Turn off oven, crack door, and let cheesecake cool for 1 hour inside.
Refrigerate for at least 4 hours before serving. Top with whipped cream if desired.