Adjust the oven rack to the center and preheat the oven to 350°F. Line the interior base and sides of a 9-inch springform pan with parchment paper or aluminum foil. Lightly apply nonstick spray. Encase the exterior base with foil and set aside.

Combine the graham cracker crumbs, processed pecans, brown sugar, and melted butter until the mixture is consistent. Firmly press this combination into the bottom and up the sides of the prepared pan, ensuring it covers at least ¾ of the pan height to adequately hold the filling and topping.

Bake for 10 minutes. Allow cooling before proceeding to the filling preparation.

Lower the oven temperature to 300ºF.

In a large bowl, blend the cream cheese with an electric mixer on medium speed until the texture is smooth, approximately 1 minute.

Integrate the sugar, sour cream, vanilla extract, and salt. Mix on medium speed until uniformly combined.

Gently fold in the eggs using a spatula. Transfer this mixture into the crust and evenly distribute it.

Bake for 40 minutes. As the cheesecake bakes, begin preparing the topping.

In a medium saucepan, combine the brown sugar, corn syrup, rum, and butter. Cook over medium heat until boiling, consistently stirring. Maintain boiling for an additional 2 minutes.

Remove from heat and allow cooling. In a separate bowl, whisk together the eggs, salt, and heavy cream.

After the cheesecake has baked for 40 minutes, retrieve it from the oven. Carefully blend the egg mixture with the cooled syrup and incorporate the chopped pecans.

Delicately layer the pecan mixture over the cheesecake. Ensure the syrup level does not surpass the crust to prevent potential seepage and resultant crust dampness.

Return the cheesecake to the oven and bake for an additional 40-50 minutes, observing until the topping achieves a golden brown hue. Should the topping edges brown excessively, cover with foil.

Upon completion, transfer the cheesecake to a cooling rack. Once fully cooled, cover and refrigerate for a minimum of 4 hours.

Carefully release the sides of the springform pan. If the sides appear adhered, utilize a butter knife to gently detach any sticking points. Subsequently, elevate the outer ring of the pan for removal.

With caution, relocate the cheesecake to a serving dish. For optimal slicing results, consider freezing the cheesecake for 1-2 hours prior to cutting.

Use a sharp knife, consistently cleaning it between slices to ensure neat portions. If the cheesecake was previously frozen, allow slices to return to room temperature for 30 minutes before serving.