Put the cookie crumbs in a small bowl and stir in the melted butter. Press the mixture in the bottom of the Springform pan.
Put the cream cheese in the bowl of an electric mixer. Using the paddle attachment, beat on medium speed for about 2 minutes, until smooth. Continuing to mix, slowly add the sugar and the salt.
Add the eggs 1 at a time and mix well. Add the ginger, cinnamon, and pumpkin purée. Decrease to low speed and stir in the mascarpone. Spread the batter over the cooked crust.
Put the cheesecake in the oven. Put a pan of hot water on another rack below the cake. (The steam prevents a crust from forming on top of the cake.)
When the cake is done, loosen it from the edges of the pan by running a knife around the inside edge. Let the cake cool for 30 minutes at room temperature. Both these steps help prevent the top from cracking. Refrigerate the cheesecake in its pan until cold.
Unmold the cheesecake by running a knife around the inside edge of the pan.
To serve the cheesecake, cut it with a hot dry knife. (Dip the knife in hot water and then dry it off.)