Preheat oven to 350 degrees F. Lightly grease and line the bottom of the 9x13-inch baking pan with parchment. I like to cut the parchment and leave extra little flaps on the sides so the bars are easy to pull out of the pan.
In the bowl of a stand-up mixer (or in a large bowl with an electric hand mixer), add the melted butter, brown sugar and white sugar. Beat until combined, about 1 minute. Next, crack in the eggs and vanilla extract; mix until combined. Add the flour, baking powder, baking soda and salt. Beat one last time until you no longer see any speckles of flour. Pour the cookie dough into the prepared pan, scraping out as much dough as possible; press the dough, spreading it to the edges with your fingers. Smooth the top as well as you can.
In the same bowl (no need to wash it out, that’s why you scraped it out!), add the cream cheese, sugar, egg and salt. Beat until mostly smooth (it might be a tad bit lumpy and that’s ok!), about 2 minutes. Pour on top of the cookie dough and smooth it out with the spatula into an even layer.
Drop small teaspoons (about 1/3 cup) of dulce de leche onto the cheesecake layer, leaving about an inch between the dollops. Using a butter knife or skewer, swirl the dulce de leche
in loopy strokes until the surface is marbled.
Transfer to the oven to bake for 25 to 30 minutes, or until the surface is only a little jiggly. Allow to cool completely, about an hour, before slicing into rectangles. Top with sprinkles of sea salt.