Preheat the oven to 350°F / 175°C. Coat a 6" cake pan with butter and sugar.
Remove the butter from the fridge. Add in the brown sugar, granulated sugar, egg yolk, milk, and vanilla and whisk until well combined.
Add in the flour, baking powder, baking soda, and salt. Use a rubber spatula to fold the cookie dough until a few flour streaks remain. Then, fold in your chocolate chips just until no flour streaks remain.
Pat the dough down into your prepared cake pan. Top with additional chocolate chips if desired. Bake the cake for 20-25 minutes, or until the edges are golden brown and the center only slightly moves when you tilt the pan.
Let the cookie cake rest in the pan for at least 20 minutes before transferring it out to fully cool.