Start by crushing the graham crackers and pecans in a food processor until finely ground. Add the brown sugar and melted butter, then mix until the texture resembles wet sand.
Press the mixture evenly into the bottom and sides of a lined springform pan. Bake the crust at 350°F for 10 minutes, then set it aside to cool.
Reduce the oven temperature to 300°F. Beat the cream cheese until smooth and creamy. Gradually add the sugar, sour cream, vanilla, and salt, mixing until well combined.
Lightly beat the eggs and fold them in gently to avoid over-aeration. Pour the filling into the crust and spread it evenly. Bake for 40 minutes until just set but slightly jiggly in the center.
While the cheesecake bakes, start the topping. Combine the brown sugar, corn syrup, rum, and butter in a saucepan over medium heat. Bring to a boil, then cook for 2 minutes before removing it from heat to cool slightly.
Whisk together the eggs, cream, and salt, then gradually add this mixture to the syrup. Stir in the chopped pecans.
Carefully spoon the pecan topping over the cheesecake, making sure not to overflow the crust. Return the assembled cheesecake to the oven and bake for an additional 50 minutes.
The edges should be golden brown. Cool the cheesecake completely before chilling it in the refrigerator for at least 4 hours, though overnight is even better.