Preheat the oven to 350F. Butter a 9½ or 10-inch springform pan and coat lightly with flour in a medium bowl, toss the gingersnap crumbs with the melted butter until evenly moistened. Press the crumbs into the bottom and 1 inch up the side of the prepared pan. Bake for about 12 minutes, or until the crust begins to color. Let the crust cool. Reduce the oven temperature to 325F.
In a large bowl, using an electric mixer, beat the cream cheese until smooth. Beat in ¾ cup of the granulated sugar and the brown sugar, then beat in the eggs in 3 additions until the mixture is thoroughly combined, scraping down the side of the bowl occasionally.
In a medium bowl, combine the Pumpkin puree and heavy cream with 1 teaspoon of the vanilla and the cinnamon, ginger and nutmeg. Add to the cream cheese mixture and beat until combined, scraping the bowl a few times.
Wrap foil loosely around the bottom and up the side of the springform pan. Pour the cheescake batter into the prepared pan and set it in a large baking dish or roasting pan. Place in the middle of the oven and pour 1 inch of hot water into the baking dish. Bake the cheesecake for about 70 minutes, or until the edges are firm and the center of the cheesecake is still slighly shaky.
In a small bowl, combine the sour cream with the remaining ¼ cup of granulated sugar and 2 teaspoons of vanilla. Remove the cheesecake from the water bath and pour on the sour cream topping. Gently top the pan to spread the topping, and continue baking the cheesecake for 10 more minutes.
Transfer the cheesecake to a rack and let cool for 1 hour. Remove the foil and the side of the pan and refrigerate the cheesecake for at least 4 hours or overnight. If you like, remove the cheesecake from the bottom of the pan by sliding a metal spatula under the crust to loosen it completely, then use 2 large metal spatulas to transfer the cake to a serving plate. Alternatively, serve the cheesecake on the pan bottom.