First, preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius) and line a 9 by 9 inch baking pan with parchment paper.

Start by making the brownie batter.  In a microwave-safe bowl, melt the butter.  Let it cool slightly.

In a large mixing bowl, combine the melted butter, granulated sugar, eggs, and vanilla extract.  Mix until well combined.

Then, add the cocoa powder, flour, salt, and baking powder to the bowl.  Stir until all the ingredients are fully incorporated and the batter is smooth.

Spread the brownie batter evenly into the prepared baking pan.  Smooth the top with a spatula.  Set aside.

Next, make the cookie dough.  In a separate mixing bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy.

Add the egg and vanilla extract to the bowl.  Mix until well combined.

In another bowl, whisk together the flour, baking soda, and salt.  Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the chocolate chips.

Drop spoonfuls of the cookie dough onto the brownie batter in the baking pan.  Use a spatula or your fingers to gently press the cookie dough down into the brownie batter.

Bake in the preheated oven for about 25 to 30 minutes or until a toothpick inserted into the center comes out with a few moist crumbs.  The brownie and cookie layers should be set.

Remove the brookies from the oven.  Let them cool in the pan on a wire rack.

Once cooled, lift the brookies out of the pan using the parchment paper as handles.  Finally, cut into squares and serve.