For the crust, place the gingersnap crumbs, sugar, butter, and nuts in a small bowl and toss lightly with a fork until well blended.
Press this mixture firmly over the bottom of a 10-inch springform pan. Bake it on the bottom oven rack until golden, 5-7 minutes, Remove it from the oven and cool.
Reduce the oven heat to 300 degrees and place a roasting pan or baking dish filled with hot water on the bottom rack of the oven to create moisture.
For the cake filling, lightly whisk together the pumpkin and spices in a small bowl until blended. Set aside.
Beat the cream cheese, sugar, and vanilla in a medium-size mixing bowl with an electric mixer on medium speed until light and fluffy, about 30 seconds. Scrape the bowl with a rubber spatula, then beat 30 seconds more.
Add the whole eggs, then the egg yolks, one at a time to the cream cheese on low speed. Blend each egg until incorporated, about 30 seconds. Scrape the bowl after each addition.
Add the pumpkin mixture to the cream cheese batter and blend on medium speed until the mixture is velvety, about 1 minute. Scrape the bowl and beat another minute.
Pour the filling over the crust. Bake the cake on the center oven rack until the top is set and a tester inserted in the center comes out dry, about 1 hour 40 minutes. Turn off the oven and leave the cake in the oven for an additional hour. Remove the cake from the oven, place it carefully on a wire rack, and let cool for several hours.
While the cheesecake is cooling, prepare the topping: Mix the sour cream and sugar together in a small bowl.
Preheat the oven to 350 degrees.
Spread the sour cream mixture evenly over the surface of the cake with a spatula and sprinkle the chopped pecans on top. Evenly space the pecan halves around the top edge of the cake.
Bake the cheesecake in the oven for 5-7 minutes to set the topping. Remove the cheesecake from the oven and refrigerate before serving.