In a bowl, combine the crushed gingersnap cookies and butter. Stir well. Pour the mixture evenly into the bottom of the spring-form pan and press firmly to create a crust.
In the bowl of a stand mixer beat the softened cream cheese until smooth. Add the sugar, and brown sugar and mix until well combined. Add the eggs and mix well. Add the pumpkin puree, vanilla, and pumpkin pie spice and mix to combine.
Pour the batter onto the crust. Lightly tap the pan on the counter to get out any air bubbles. Bake until the edges are set. Turn off the heat, crack open the door to the oven, and allow the cheesecake to cool in the oven
Remove from the oven and cool completely, then remove the outer ring of the springform. Refrigerate overnight to allow the cheesecake to firm up before serving.
In a medium saucepan, combine the butter, brown sugar, corn syrup, and heavy cream. Cook until bubbly, then stir in the toasted pecans, salt, and vanilla. Cool to room temperature and thick before pouring over the cooled cheesecake.