Preheat oven to 350 degrees.
Line 9x13 pan with foil, folding excess over the sides.
Mix together the melted butter, sugar, vanilla and salt. Add flour and mix just to combine. Press the dough evenly the bottom of the pan. Bake 20-25 minutes, or until crust is golden brown, with the edges slightly darker than the center. Let cool on a wire rack.
LOWER the oven temperature to 325 degrees.
While crust is cooling, mix in 1/8 teaspoon salt into 1/2 cup dulche de leche. Set aside.
In bowl of electric mixer, beat cream cheese until smooth and creamy, about 5 minutes on medium speed.
Beat in sugar and vanilla. Add eggs one at a time, beating well after each.
Scrape down the bowl and beat until batter is completely smooth and well blended. Stir in 2-3 tablespoons of cheesecake batter into the salted dulche de leche.
Pour the remaining cheesecake batter over the cooled crust. Dollop the dulce de leche mixture over the cheesecake batter, leaving plenty of cheesecake batter in between. Using a knife, swirl the dulce de leche into the cheesecake batter in small circles until the surface is nicely marbled. Bake 20-30 minutes, or until the filling is puffed but still jiggles like Jell-o when the pan is nudged.
Set the pan on a cooling rack and let cool completely. Refrigerate for at least 4 hours but preferably 24 hours before cutting into squares and serving. Keep leftovers refrigerated in an airtight container for up to 3 days.