Preheat your oven to 325 degrees F. Line a 9×9-inch baking pan with parchment paper, then spray with cooking spray. Set aside.
In a small microwave-safe bowl, melt the butter until completely melted. It's helpful to heat it in 30-second intervals until fully melted. Set aside to cool.
Prepare the boxed brownie mix according to the package instructions. This usually involves combining the mix with eggs, oil, and water. Mix until well combined and set aside.
In a medium-sized bowl, combine the melted and cooled butter with the brown sugar. Aim for a smooth and creamy consistency when mixing, about 30 seconds.
Whisk in the eggs and egg yolk, one at a time, until well combined and smooth. This ensures the mixture is well combined and smooth. Mix the cake batter extract, vanilla extract until combined.
With a rubber spatula, fold in cornstarch, baking powder, salt, and flour into the wet ingredients. It's recommended to sift the flour, cornstarch, and baking powder together before adding them to the wet ingredients to prevent lumps and ensure even distribution. Add the chocolate chips and rainbow sprinkles, and mix until no streaks of flour remain. Avoid overmixing the batter to prevent toughness.
Using two spoons or a cookie scoop, alternate between the brownie batter and cookie dough by dropping small balls or dollops into the prepared pan. Aim for a consistent size for the dollops, such as using a tablespoon or cookie scoop for consistency. It’s okay if it doesn’t look smooth on top. As it bakes, it will even out.
Bake in the preheated oven for 50-55 minutes, depending on your oven, or until a toothpick inserted into the center comes out with moist crumbs. The brookies should be set around the edges but still slightly soft in the center.
Let the brookies cool completely in the pan on a wire rack, which can take up to 30 minutes, to allow them to set up properly.