1. Preheat the oven to 350°F (175°C). Line and spray a 9-inch springform pan, wrapping the bottom in foil to prevent leaks.
2. Combine graham cracker crumbs, ground pecans, brown sugar, and melted butter until the mixture resembles wet sand. Press into the bottom and up the sides of the pan. Bake for 10 minutes, then cool slightly.
3. Reduce oven temperature to 300°F (150°C). Beat the cream cheese until smooth. Add granulated sugar, sour cream, vanilla, and salt, mixing until combined. Fold in the eggs gently. Pour this filling into the cooled crust and bake for 40 minutes until the center is set.
4. For the topping, melt brown sugar, corn syrup, rum, and butter in a saucepan over medium heat, boiling for 2 minutes, then allow cooling.
5. In a bowl, whisk together the eggs, heavy cream, and salt. Gradually combine with the cooled syrup mixture, then stir in the pecans.
6. Carefully spoon the pecan topping over the cheesecake, ensuring the syrup is added gradually to avoid overflow. Bake for an additional 40-50 minutes until golden brown.
7. Cool the pie completely before refrigerating for at least 4 hours or overnight before serving.