Preheat your oven to 350°F (175°C). In a medium bowl, combine the gingersnap crumbs and sugar, then pour in the melted butter. Mix until the mixture resembles wet sand and holds together when pressed.
Transfer the crust mixture to a 9-inch pie dish and press firmly against the bottom and sides, creating an even layer. Use the bottom of a measuring cup to press the crust for a more compact base.
Bake the crust for 8-10 minutes until it's slightly set and fragrant. Remove from the oven and allow to cool slightly. Reduce oven temperature to 325°F (165°C).
In a large bowl, beat the cream cheese until smooth and fluffy, about 2 minutes. Add the sugar and continue beating until well incorporated and no lumps remain.
Beat in the egg and vanilla extract until just combined. Avoid overmixing to prevent incorporating too much air.
In another bowl, whisk together the pumpkin puree, heavy cream, eggs, brown sugar, pumpkin pie spice, and salt until completely smooth and uniform in color. Tap the bowl gently on the counter to release any trapped air bubbles.
Pour the cheesecake mixture into the pre-baked crust, spreading it evenly with a spatula.
Gently spoon the pumpkin mixture over the cheesecake layer, being careful not to disturb the bottom layer. Smooth the top with a spatula.
Place the pie on the middle rack of your oven and bake for 50-55 minutes. The pie is done when the edges are set but the center still has a slight jiggle.
Allow the pie to cool completely on a wire rack for about 2 hours, then refrigerate for at least 4 hours or overnight.