Place gingersnap cookies in a food processor and pulse until finely crushed into crumbs.
Pour the melted butter over the cookie crumbs and stir with a spatula until evenly coated and mixture is moist.
Press the crumb mixture firmly into the bottom of an 8-inch springform pan, creating an even crust layer. Chill briefly while preparing the filling.
In a large mixing bowl, beat the softened cream cheese until smooth and fluffy, about 2-3 minutes.
Add the granulated sugar and continue beating until combined and creamy, about 2 minutes.
Mix in the canned pumpkin, cinnamon, ginger, and salt, blending until the mixture is smooth and well incorporated.
One at a time, beat in the eggs, mixing well after each addition and ensuring a silky, even batter forms.
Pour the pumpkin filling over the chilled crust, smoothing the top with a spatula for an even surface.
Bake in a preheated oven at 325°F (160°C) for about 60 minutes, or until the edges are set but the center slightly jiggles when gently shaken.
Remove from the oven and let the cheesecake cool completely in the pan on a wire rack, then refrigerate for at least 4 hours or overnight for best flavor and texture.
Carefully remove the springform pan’s sides, revealing a smooth, spiced pumpkin cheesecake with a crunchy crust, ready to slice and serve.