Place one oven rack in the upper third of the oven and one rack on the bottom. Place a 9x13 metal pan on the bottom. Preheat oven to 300 degrees. Line the bottom of a 9-inch spring-form pan with parchment paper.
In a food processor or blender, blend cookies into crumbs. Add sugar and butter and blend until combined. Empty into the bottom of a pan. Spread and firmly press crumbs down and a little up the sides. Bake for 15 minutes.
For the White Chocolate Cheesecake:
Place chopped chocolate in a bowl with the half and half cream. Microwave at medium power for 30 seconds at a time, stir, and heat another 30 seconds. Mix until all chocolate is melted and smooth. Let cool for a few minutes.
Using an electric mixer, blend the cream cheese until smooth. Mix in the sugar and then one egg at a time. Mix in the vanilla and then the melted chocolate. Set aside.
For the Pumpkin Cheesecake:
Using an electric mixer, blend the cream cheese until smooth. Mix in the sugar and then the pumpkin puree and spices. Mix in one egg at a time until combined.
For Assembling:
Pour large dollops of alternating batters side-by-side, in one layer and again for a second layer. Used a knife to swirl layers together.
Heat 3 cups of water to boiling. Pour the water in the pan that is in the bottom of the oven and then immediately place the cheese cake on the upper rack. Bake for 55 minutes. Turn off the oven, let it sit in there for 30 minutes, then crack the door about 1 inch and let it sit in there for another 30 minutes. Remove from the oven and allow to cool completely before refrigerating. Refrigerate overnight.
Run knife along edges of pan and remove side of pan. Slide a long metal spatula under the parchment paper and remove cake onto serving platter. Add toppings, slice, and serve.
For the Topping:
Whip powdered sugar and cream together until stiff peaks. Place in a piping bag and pipe onto the edges of the cake.
Melt the chocolate, pour onto the back of a cookie sheet and spread as thin as possible. Place in freezer for 1-2 minutes until you can touch it without leaving a finger print. Use a metal spatula to push the chocolate off and create shaving.