Mix the melted butter, cookie crumbs, and chopped pecans in a medium bowl. Transfer to a 9-inch springform pan and press into the bottom.Set springform pan on a piece of heavy duty aluminum foil and press the aluminum foil up onto the sides of the pan. This will help keep anything from leaking out.Bake for 8 to 10 minutes. Let cool.
In a large bowl, use an electric mixer to beat cream cheese until smooth. Gradually beat in granulated sugar and brown sugar.
Beat in the eggs one at a time.
Add pumpkin puree and beat until mixed in.
Add heavy cream, pumpkin pie spice, vanilla, and salt and beat just until mixed in.
Pour batter into prepared crust.Place on a rimmed baking sheet and bake for 1 hour. Turn oven off and use a wooden spoon to crack oven door open. Leave cheesecake in oven for another 50 to 60 minutes.
Refrigerate cheesecake for at least 12 hours.
Make Caramel Sauce. In a medium saucepan, heat brown sugar, butter, and heavy cream over medium heat. Simmer for about 5 to 6 minutes, whisking frequently. Remove from heat and stir in vanilla and salt. Let cool. Refrigerate until needed.
Slice cheesecake and serve with whipped cream and caramel sauce.