Melt the unsalted butter in a saucepan over medium heat, stirring often for about six minutes until it turns golden brown. Let it cool for about five minutes.
Pour the cooled butter into an electric mixer, add granulated sugar and packed brown sugar, and mix on low until combined. Let cool a few more minutes.
In a separate bowl, combine all-purpose flour, baking soda, and salt. Stir with a whisk or spatula to ensure even distribution.
Add the eggs one at a time to the butter-sugar mixture, mixing completely after each addition. Then mix in the pure vanilla extract.
Gradually add the flour mixture to the wet ingredients in the mixer and mix until just combined. Fold in the chocolate chips using a spatula.
Line a 9x13” baking pan with foil and spray lightly with cooking spray.
Press half of the cookie dough into the bottom of the prepared pan, pour sweetened condensed milk over it, scatter chocolate bar pieces on top, and crumble the remaining dough over it.
Preheat the oven to 350°F and bake for about 30-35 minutes until the tops turn golden brown. Let cool completely before slicing.