Heat oven to 325°F In a food processor, pulse the gingersnaps until fine crumbs form (you should have about 1 cup). Add the melted butter and pulse to combine. Press the mixture into the bottom of a 9-inch srpingform pan (preferably nonstick), using a straight sided dry measuring cup to help. Spray the sides of the pan lightly with cooking spray. Place the pan on a rimmed baking sheet.
Using an electric mixer, beat the cream cheese and brown sugar on medium until smooth, 1 to 2 minutes. Beat in the eggs, one at a time. Add the flour, alspice, ginger, cinnamon, and salt and beat to combine. Add the pumpkin and beat to combine. Pour the mixture into the prepared pan, tent loosely with foil and bake until set but slightly wobbly in the center, 75 to 105 minutes.
Let cool completely in the pan, then refrigerate until firm, at least 2 hours. Run a knife around the edge of the pan to loosen, then unmold.
Just before serving, using an electric mixer, beat the cream, sour cream and confectioners' sugar until soft peaks form. Dollop on the cheesecake and dust with cinnamon.
To prep ahead: The cheesecake can be baked up to 2 days in advance (do not top with the sour cream mixture); refrigerate, covered.
To serve: Let sit at room temperature for 1 hour before serving. Make the sour cream mixture, dollop it on the cheesecake, and dust with cinamon just before serving.