Preheat the oven to 350°F and line an 8-inch square pan with parchment paper. Stir the gingersnap cookie crumbs with the melted butter until evenly moistened, then press the mixture firmly into the bottom of the pan to form the crust.
In a mixing bowl, beat the softened cream cheese until smooth. Add the pumpkin puree, granulated sugar, egg, vanilla extract, cinnamon, nutmeg, and ginger. Mix until the filling is fully combined and free of lumps.
Pour the pumpkin cheesecake mixture over the prepared crust and spread it into an even layer. Bake for 25 to 30 minutes until the edges look set and the center still has a slight jiggle.
Remove the pan from the oven and let the bars cool at room temperature for 30 minutes. Transfer to the refrigerator and chill for at least 2 hours before slicing into four squares.