Preheat oven to 350 degrees. Coat a 9-by-13-inch rimmed baking sheet with cooking spray; set aside. Place gingersnaps in a food processor; pulse to a powder. Transfer to a small bowl, and stir in butter until well combined. Press gingersnap mixture evenly into bottom of prepared baking sheet. Bake crust until firm, about 12 minutes. Let cool completely.
Meanwhile, put cream cheese in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until softened. Mix in sugar, egg, egg yolk, sour cream, and vanilla until well combined. Mix in crystallized ginger.
Pour the cream cheese mixture onto crust, and spread evenly with a rubber spatula. Bake, rotating sheet halfway through, until filling has puffed and feels slightly firm to the touch (do not let brown), 20 to 25 minutes. Let cool completely on a wire rack. Refrigerate, covered with plastic wrap, until set,
about 1 hour. To serve, cut into bars. Bars can be refrigerated in single layers in airtight containers up to 2 days.