Preheat your oven to 350°F (175°C). Line a 9x9 inch baking pan with parchment paper, leaving an overhang on two sides.
Melt the butter in a large bowl and whisk in the cocoa powder until smooth. Whisk in the sweetened condensed milk and vanilla, fold in the flour, baking powder and salt, then spread the brownie batter evenly into the pan.
In another bowl, beat the softened butter with the brown sugar and granulated sugar for about 2 minutes, until light and creamy. Beat in the milk and vanilla.
Add the flour, cornstarch, baking soda and salt and mix on low speed just until a soft dough forms. Fold in the chocolate chips.
Pinch off walnut-sized pieces of cookie dough, flatten them slightly between your palms and arrange them over the brownie batter. Cover most of the surface, leaving small gaps so some brownie peeks through.
Bake for 35 to 40 minutes, until the cookie layer is golden and a toothpick inserted into a brownie section comes out with moist crumbs.Check at 25 minutes, and if the top is browning too quickly, loosely cover the pan with foil for the remaining time.
Let the brookies cool completely in the pan, at least 2 hours, before lifting them out and cutting into 16 squares. They are very soft while warm and set up beautifully as they cool.