Adjust the oven rack so it sits in the center of the oven and preheat to 350°F (177°C). Line the bottom and sides of a 9-inch springform pan with parchment paper or aluminum foil, then lightly mist the inside with nonstick spray. Wrap another layer of foil snugly around the outside of the pan to protect the crust from any leaks and set the pan aside.

In a mixing bowl, combine the graham cracker crumbs, finely ground pecans, brown sugar, and melted butter. Stir until every crumb is evenly moistened and the mixture resembles damp sand. Press this mixture firmly into the bottom and up the sides of the prepared pan. There should be enough crust to come at least three-quarters of the way up the sides so it can contain both the cheesecake filling and pecan topping.

Bake the crust for 10 minutes, then remove it from the oven and place it on a wire rack to cool slightly while you prepare the filling.

Reduce the oven temperature to 300ºF (149°C).

In a large bowl, beat the softened cream cheese with an electric mixer on medium to medium-high speed until it’s completely smooth and free of lumps, about 1 minute. Scrape down the sides and bottom of the bowl as needed. Add the granulated sugar, sour cream, vanilla extract, and salt. Continue mixing on medium speed until the mixture is creamy and well blended.

Switch to a silicone spatula and gently fold in the lightly beaten eggs just until they are incorporated. Avoid overmixing at this stage to keep excess air out of the batter. Pour the cheesecake batter into the cooled crust, using an offset spatula to spread it into an even layer.

Bake for 40 minutes. As soon as the cheesecake goes into the oven, start preparing the topping so it has time to cool slightly before you add it.

In a medium saucepan, combine the brown sugar, dark corn syrup, dark rum, and butter. Place over medium heat and cook, stirring constantly, until the mixture comes to a full boil. Allow it to boil for 2 minutes while stirring to prevent scorching. Remove the pan from the heat and let the mixture cool while the cheesecake continues baking.

In a separate bowl, whisk together the eggs, salt, and heavy cream until smooth. Set this mixture aside until the sugar syrup has cooled slightly.

After the cheesecake has baked for 40 minutes, carefully take it out of the oven. Slowly whisk the egg and cream mixture into the cooled sugar syrup until everything is fully combined and glossy. Stir in the chopped pecans, making sure they are evenly coated.

Using a spoon, gently distribute the pecan topping over the surface of the partially baked cheesecake. Start by spooning the pecans themselves over the top, then add just enough of the syrup to fill the crust without going above the crust line. Keeping the topping contained within the crust helps prevent it from seeping underneath and softening the crust or gluing the springform ring to the base.

Return the pan to the oven and bake for an additional 40–50 minutes, or until the pecan topping is golden brown and crisp on top. If you notice the edges of the pecan layer browning too quickly, tent them loosely with foil to prevent over-browning.

Transfer the cheesecake to a wire rack and let it cool completely at room temperature. Once cooled, cover the pan and refrigerate for at least 4 hours, or overnight, to allow the cheesecake to fully set.

When you’re ready to unmold, carefully loosen the sides of the springform pan. If the topping has slightly adhered to the sides, gently run a butter knife between the cheesecake and the pan to release it, then press up from the bottom of the pan to separate the base from the ring. Lift away the outer ring.

Slide the cheesecake onto a serving platter. For especially clean, neat slices, place the cheesecake in the freezer for 1–2 hours before cutting.

To slice, run a sharp knife under hot water, then dry the blade thoroughly. Make the first cut with a smooth, steady motion. Rinse and warm the knife again, dry it, and continue cutting, repeating this step for each slice to keep the edges tidy. If the cheesecake was frozen before slicing, let the slices rest at room temperature for about 30 minutes before serving so the texture softens to a creamy, velvety consistency.