Preheat the oven to 350°F and line two large baking sheets with parchment paper. Set them aside.
To prepare the brownie cookie dough, beat the butter and brown sugar together in the bowl of a stand mixer for about 3 minutes, until light and fluffy. Add the egg and vanilla, mixing until well combined. In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt. Sift the dry ingredients into the egg and butter mixture, then mix on low speed until combined and the flour is fully incorporated. Stir in the chocolate chips with a large spatula. Set the dough aside while you prepare the chocolate chip cookie dough.
For the chocolate chip cookie dough, combine the cold butter, brown sugar, and granulated sugar in the bowl of a stand mixer fitted with the paddle attachment. Start mixing on low speed and gradually increase the speed to cream the butter and sugars together for 4 minutes, until pale and fluffy. The mixture should have no visible chunks of butter. Scrape down the sides of the bowl as needed.
Add the egg and egg yolk one at a time, stopping to scrape down the bowl between additions. Mix in the vanilla extract. In a separate bowl, whisk together the flour, baking soda, cornstarch, and salt. Gradually add the dry ingredients to the butter and egg mixture in two additions, mixing on low speed until just combined. Be careful not to overmix. Stir in the chocolate chips using a large spatula, again being careful not to overmix.
Using a small cookie scoop, scoop the dough into balls, making the chocolate chip cookie dough balls slightly larger than the brownie cookie dough balls. Roll them into uniform balls using your hands. For even-sized cookies, you can use a kitchen scale to weigh the dough balls. It may be easiest to roll all the brownie cookie dough balls first, followed by the chocolate chip cookie dough balls.
Take one brownie cookie dough ball and one chocolate chip cookie dough ball, press them together, and roll them into a single ball using your hands. Place the dough balls on the prepared baking sheet, spacing them about 2 inches apart.
Bake one sheet at a time in the center of the oven for 8 to 9 minutes, or until the edges are set and the tops are fluffy and slightly underbaked. Avoid overbaking. Once done, remove the cookies from the oven and let them cool on the cookie sheet for 5 to 10 minutes before transferring them to a wire rack to cool completely. Repeat with the remaining doughs, allowing the cookie sheet to cool between batches.
If desired, sprinkle the cooled cookies with flaky sea salt before serving.
Note: Depending on the ratio of chocolate chip dough to brownie dough used, you may have some chocolate chip cookie dough left over. You can bake any leftover dough at the end.