When the cookies are almost done chilling, start the brownie batter. Preheat the oven to 325F. Spray a 9X9 pan with non-stick baking spray. Line the bottom and 2 sides of the pan with parchment paper. This will make it easier to take out of the pan.
In a medium bowl, whisk the flour, cocoa powder, cornstarch, and salt. Set aside.
Using a mixer, combine sugar, eggs, and egg yolk. Use a whisk attachment and beat for 5 minutes. Melt the butter while this beats so it can cool down slightly. Egg mixture will be very light and fluffy.
Add in melted butter, oil, and vanilla. Mix on low until combined. Take off mixer. Add in all of the dry ingredients. Use a rubber spatula and fold in the dry ingredients. Be gentle to not knock any air out of the eggs. Add in the chocolate chips, and milk chocolate chips.
Pour the batter in the pan. Use a rubber spatula to smooth the batter into the corners.
Bake for 15 minutes for the brownie top to be set slightly before adding the cookie dough. Take dough out of the fridge. And take small handfuls of dough, and flatten into a disc shape. Top the brownies with the cookie dough discs. Continue until all of the dough is used
Bake for another 20 minutes. Top with foil loosely to protect the cookie from over browning. Bake for another 5-10 minutes until the cookie and brownie is set. There should be no jiggle. Place brownies on cooling rack.
Let the brownies cool completely. They should be completely room temperature before cutting into. Store at room temperature.