In a small bowl, sprinkle the gelatin over the water and let stand for 5 minutes. In a large bowl, whisk the yolks, cornstarch, salt and 1 1/2 cups of the sugar until the sugar is moistened. In a large saucepan, heat the milk just until steaming. Whisk 1 cup of the hot milk into the yolk mixture. Pour the mixture into the milk in the saucepan and cook over moderate heat, whisking constantly, until boiling and thick, about 5 minutes. Whisk in the pumpkin puree and cook, whisking, for 1 minute. Off the heat, whisk in the gelatin, vanilla and cinnamon. Whisk in the mascarpone.
In a small microwave-safe bowl, microwave the Calvados with the remaining 1 tablespoon of sugar at high power for 10 seconds, just until the sugar is dissolved.
Arrange one-third of the whole gingersnaps in a 9-by-13-by-2 1/2-inch baking dish. Lightly brush the gingersnaps with some of the Calvados and top with one-third of the pumpkin custard. Repeat the layering twice more with the remaining whole gingersnaps, Calvados and custard. Sprinkle half of the crushed gingersnaps on top and press a sheet of plastic wrap directly on the surface of the tiramisù. Freeze overnight.
Let the tiramisù stand at room temperature for 6 hours, until thawed. Sprinkle with the remaining gingersnaps. Serve.
The pumpkin tiramisù can be frozen for up to 1 week. Thaw at room temperature for 4 to 6 hours or overnight in the refrigerator.