Preheat your oven to 350F. Line an 8x8 inch baking pan with parchment paper, leaving overhang on two sides.
In a large bowl, beat the softened butter, brown sugar, and granulated sugar with an electric mixer until light and fluffy, about 2 minutes. Add the egg and vanilla extract and beat until combined.
Add the flour, baking soda, and salt. Mix on low speed until just incorporated. Fold in the chocolate chips with a spatula.
Press about two-thirds of the cookie dough evenly into the bottom of the prepared pan. It helps to dampen your fingers slightly to prevent sticking.
Spread the entire can of dulce de leche evenly over the cookie dough base, leaving a very thin border around the edges.
Take small pieces of the remaining cookie dough and flatten them between your palms. Lay them over the dulce de leche layer, covering as much surface as you can. Small gaps are perfectly fine as the dough will spread in the oven.
Bake for 28 to 32 minutes, until the top is golden brown and the edges are set. Let the bars cool completely in the pan, then refrigerate for at least 1 hour to allow the dulce de leche to firm up. Sprinkle with flaky sea salt before slicing.