Melt butter in a saucepan over medium heat. Cook, stirring often, about 6 minutes, until it becomes brown in color. It will foam, reduce, then foam again. Once it’s done cooking the foam is a light brown and it will dissipate after you remove it from the heat. Once it starts to brown, keep stirring so it doesn’t burn. Let sit for about 5 minutes to cool.
Pour into an electric mixer fitted with paddle attachment. While still hot, add both sugars and mix on low until combined. Let sit to cool for a few minutes.
While butter mixture is cooling, combine flour, baking soda, and salt in a medium bowl. Stir and set aside.
Turn mixer (with butter mixture bowl attached) on low. Add eggs, one at a time, mixing completely. Mix in vanilla extract. Add flour mixture to the wet ingredients and mix until combined. Stir in chocolate chips.
Line a 9x13” baking pan with foil and spray with cooking spray for easy removal.
Press half the cookie dough in the prepared pan. Pour sweetened condensed milk over the top of the bottom layer (be careful to leave about 1/4” edge around the pan so the milk doesn’t touch the foil), then break up the chocolate bar and drop pieces over the top. Break up the remaining cookie dough and place on top of milk. Press with your hands to flatten. It will mostly cover but not completely cover the bottom layer.
Refrigerate pan for 30 minutes.
Preheat oven to 350°F. Bake for about 30-35 minutes until the tops of the bars start to get golden brown. Cool completely before slicing into bars.