Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, finely ground pecans, brown sugar, and melted unsalted butter. Stir until the mixture resembles wet sand. Press this mixture firmly into the bottom of a 9-inch springform pan to create an even layer. Bake for 10 minutes, then remove and allow to cool completely before adding the filling.

Once the crust has cooled, reduce the oven temperature to 300°F (150°C). In a large mixing bowl, beat the softened cream cheese until smooth and creamy. Gradually mix in granulated sugar, sour cream, vanilla extract, and salt until fully combined. Carefully add lightly beaten large eggs, folding them in gently to maintain a fluffy texture. Pour the cheesecake filling into the cooled crust, spreading it evenly.

In a medium saucepan over medium heat, combine light brown sugar, dark corn syrup, dark rum, and unsalted butter. Stir the mixture constantly until it begins to boil, then let it boil for about 2 minutes. Remove from heat and allow the syrup to cool slightly. In a separate bowl, whisk together eggs, heavy cream, and a pinch of salt to create the pecan topping mixture.

After the cheesecake has baked for 40 minutes, carefully pour the egg mixture into the cooled syrup, stirring in the coarsely chopped pecans. Gently spoon the pecan topping over the baked cheesecake, taking care not to let excess syrup overflow past the crust. Return the cheesecake to the oven and bake for an additional 40 to 50 minutes, until the topping is golden brown and slightly puffed.

Once baked, remove the Pecan Pie Cheesecake from the oven and let it cool completely at room temperature. After it has cooled, refrigerate it for at least 4 hours, or overnight for best flavor and texture. When ready to serve, use a sharp knife warmed under hot water for clean slices and enjoy this delightful dessert with family and friends.