Preheat the oven to 350°F (177°C) and prepare a 9-inch springform pan by lining with parchment paper and spraying with nonstick spray.
Wrap the bottom of the pan with foil to prevent leaks.
Mix graham cracker crumbs, ground pecans, brown sugar, and melted butter until the mixture resembles wet sand. Press into the pan.
Bake the crust for 10 minutes, then set aside to cool. Reduce oven temperature to 300°F.
Beat cream cheese until smooth, then add sugar, sour cream, vanilla extract, and salt. Mix until creamy, then fold in eggs.
Pour filling into crust.
For a water bath, place a large pan with 1 inch boiling water on a lower oven rack.
Bake the cheesecake on the middle rack for 55–70 minutes until set.
Prepare the topping by melting brown sugar, corn syrup, rum, and butter. Cool, then whisk with eggs, heavy cream, and salt.
Toast pecans at 300°F for 8–10 minutes until fragrant.
Spread topping over the cheesecake and bake for another 40–50 minutes until crisp.
Cool completely, then refrigerate at least 4 hours or overnight before serving.