BROWNIE LAYER: Preheat the oven to 350 degrees. Spray an 8x8-inch pan with nonstick spray. Line with a strip of parchment paper so that it covers the bottom and comes up two sides of the pan. Spray the parchment with nonstick spray too.
In a large microwave safe bowl, microwave the butter and chocolate chips together, stirring every 30 seconds, until melted and smooth. Whisk in the sugar, brown sugar and vanilla. Whisk in eggs one at a time, until incorporated.
Sift flour and salt into the bowl, stir until combined. Scrape the brownie batter into the prepared baking pan. Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Remove pan to a cooling rack; cool completely before adding the cookie dough layer.
COOKIE DOUGH: In a large bowl, using an electric mixer, beat butter, sugar, brown sugar, milk and vanilla until creamy. Add flour, beat until combined. Stir in 1 cup of chocolate chips. Spread the cookie dough onto a sheet of parchment paper, use your hands to shape the dough into a 8x8-inch square. Lift the square and place it over the brownies, gently pressing it into place. Sprinkle the top with additional chocolate chips if desired.
Cook's Note: For easy cutting, chill the brownies for 1 to 2 hours before cutting. Run a knife along the sides of the brownie pan, then use the parchment paper to lift the brownies from the pan and onto a cutting board. Slice the brownies with a sharp knife, wiping the knife with a paper towel between cuts.