Preheat oven to 350°F (175°C) and line a standard 12-cup muffin tin with paper liners.
In a small bowl, combine gingersnap crumbs and melted butter until moistened.
Press 1 tablespoon of the mixture into the bottom of each liner and bake for 5 minutes. Remove and let cool.
In a large bowl, beat the softened cream cheese and sugar until smooth and creamy.
Add pumpkin puree, egg, vanilla extract, and pumpkin pie spice, mixing on low speed until just combined.
Divide the cheesecake batter evenly among the 12 muffin cups.
Bake for 18 to 22 minutes or until the edges are set and the centers slightly jiggle.
Cool completely at room temperature, then refrigerate for at least 3 hours before serving.