Preheat the oven to 300 degrees F. Line 18 muffin cups, from 2 12-cup muffin tins, with paper liners. Place 1 whole cookie in the bottom of each lined cup.
Beat the cream cheese, granulated and brown sugars and 1/4 teaspoon salt in a large bowl using an electric mixer on medium-high speed until smooth and creamy, 2 to 3 minutes, stopping to scrape down the sides of the bowl as needed. Reduce the speed to low and beat in the eggs until combined. Beat in the half-and-half and sour cream until smooth. Use a spatula to stir in the pumpkin puree and pumpkin pie spice until well blended. Divide the batter evenly among the cookie-lined cups (the cups will be very full).
Bake until the filling is just set and a knife inserted into the center comes out moist but clean, 40 to 45 minutes. Cool completely in the pans on a wire rack and then refrigerate until cold, at least 4 hours or up to overnight. Top each with whipped cream and a sprinkle of crystallized ginger before serving.
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