Make the crust: Preheat oven to 375°F. Process gingersnaps in a food processor until fine crumbs form, 20 to 25 seconds. Add brown sugar, salt, and ground ginger; pulse to combine, 5 or 6 times. Add butter and pulse until combined, 10 to 12 times. Press in bottom and up sides of a 9-inch deep-dish pie plate. Freeze 30 minutes. Bake until dry to the touch and fragrant, 12 to 14 minutes. Cool completely on a wire rack.
Make the filling: Reduce oven temperature to 350°F. Whisk together granulated sugar, ground ginger, cinnamon, salt, and cloves in a bowl until combined. Whisk in pumpkin, half-and-half, eggs, and fresh ginger just until combined. Pour into prepared crust.
Bake until filling is set (it may jiggle slightly in very center), shielding crust with foil after 30 minutes to prevent excessive browning, 60 to 70 minutes. Cool completely on a wire rack. Serve at room temperature or chilled, topped with whipped cream and candied ginger.
