Crust: Preheat oven to 350 degrees. Pulse gingersnaps and sugar in a food processor until fine crumbs form. Add butter and pulse to combine. Press mixture evenly into bottom and up sides of a 9-inch pie dish. Freeze until firm, about 30 minutes.
Bake crust until golden in spots, about 15 minutes. With the bottom of a measuring cup, gently flatten bottom and sides of crust. Let cool completely on a wire rack. Reduce oven temperature to 325 degrees.
Filling: Pulse cream cheese in food processor until smooth. Add sugar and pumpkin and process until smooth, occasionally scraping down sides of bowl. Add egg and yolk, flour, salt, cinnamon, ginger, and cloves; process until incorporated.
Pour filling into cooled shell and bake until custard is just set, about 33 minutes. Let cool completely on a wire rack, then refrigerate until cold and firm, at least 4 hours and up to overnight.