Line an 8x8 inch baking pan with parchment paper, leaving some overhang on the sides for easy removal.
In a medium bowl, combine the graham cracker crumbs and 1/3 cup granulated sugar and stir to blend.
Pour in the melted butter and mix until all the crumbs are evenly moistened and the mixture looks like wet sand.
Transfer the crumb mixture to the prepared pan and press it firmly and evenly into the bottom using the bottom of a measuring cup or glass.
Place the pan in the freezer for 10 to 15 minutes to help the crust set while you prepare the filling.
Preheat the oven to 325°F.
In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until completely smooth and creamy, about 1 to 2 minutes.
Gradually add the remaining 2/3 cup granulated sugar, beating until the mixture is light and fluffy and no graininess remains.
Add the eggs one at a time, mixing on low speed just until each egg is incorporated and scraping down the sides and bottom of the bowl as needed.
Add the vanilla bean paste and mix on low speed until evenly combined and the batter is smooth.
Remove the crust from the freezer and pour about two-thirds of the cheesecake batter over the chilled crust, spreading it into an even layer with a spatula.
If the dulce de leche is very thick, warm it briefly in the microwave for 10 to 15 seconds until it is pourable but not hot.
Drizzle or spoon most of the dulce de leche evenly over the cheesecake layer in the pan.
Dollop the remaining cheesecake batter over the top in several spoonfuls, leaving some of the dulce de leche showing through.
Use a thin knife or skewer to gently swirl the cheesecake batter and dulce de leche together in figure-8 or “S” motions to create a marbled pattern without overmixing.
Tap the pan lightly on the counter to release any large air bubbles and to level the surface.
Bake the bars at 325°F for 30 to 35 minutes, or until the edges are set and the center still has a slight wobble when you gently jiggle the pan.
Remove the pan from the oven and place it on a wire rack to cool completely to room temperature, 1 to 2 hours.
Once cooled, cover the pan loosely with plastic wrap or foil and refrigerate for at least 4 hours or preferably overnight until fully chilled and firm.
Just before serving, sprinkle the top with a pinch of flaky sea salt and chopped pecans or walnuts if using.
Use the parchment overhang to lift the chilled cheesecake slab out of the pan and place it on a cutting board.
With a sharp knife, cut into 16 even bars, wiping the knife clean between cuts for the neatest slices.
Serve chilled and store any leftovers covered in the refrigerator.