Preheat oven to 350F. Wrap the outside of a 9-inch springform pan tightly with two layers of heavy-duty foil. Stir together gingersnap crumbs, melted butter, and sugar until the texture of wet sand. Press firmly into the bottom and 1 inch up the sides of the pan. Bake 8 minutes until set, then cool on a rack. Reduce oven to 325F.

Heat the heavy cream in a small saucepan until steaming. Pour over the chopped chocolate in a bowl, let sit 2 minutes, then stir until completely smooth. Set aside to cool slightly.

Beat cream cheese, granulated sugar, and brown sugar on medium speed until completely smooth and fluffy, about 3 minutes, scraping the bowl twice. Beat in pumpkin, sour cream, and vanilla until incorporated. Add eggs one at a time, beating just until blended after each addition. Finally mix in cinnamon, ginger, nutmeg, and salt until just combined. Do not overbeat.

Pour two-thirds of the filling into the cooled crust. Drizzle half the chocolate over the surface, then use a knife to swirl it through the filling. Pour remaining filling on top, drizzle with remaining chocolate, and swirl again. Place the springform pan in a large roasting pan and pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan. Bake 55-65 minutes until the edges are set but the center 2 inches still jiggle slightly when nudged.

Turn off the oven, crack the door open with a wooden spoon, and let the cheesecake cool in the water bath for 1 hour. Remove from the water bath, run a thin knife around the edge to loosen, and cool completely on a rack. Cover and refrigerate at least 6 hours or overnight before removing the pan sides and slicing.