In a medium bowl, combine the butter and crushed gingersnaps. Press the mixture into a 9-inch springform pan, working the crumbs over the bottom and then up the sides. Bake for 20 minutes.
In a small bowl, toss the pears and ginger. Line the cooled crust with the pears, overlapping the slices slightly.
In a large bowl, with an electric mixer on medium, beat the cream cheese for 2 minutes. Add 1 cup of the sugar and beat for 2 minutes. Add the eggs, 1 at a time, and mix until combined. Stir in 2 teaspoons of the vanilla. Pour the mixture over the pears. Bake until the top is barely set but still slightly wobbly, about 50 minutes. Transfer pan to a wire rack but leave oven on.
In a small bowl, combine the sour cream and the remaining sugar and vanilla. Pour over the cheesecake and bake for 8 minutes. Transfer to a wire rack and cool to room temperature. Cover and refrigerate for at least 4 hours before serving.