Preheat and Prep the Pan: Preheat your oven to 350°F (175°C). Lightly grease a 9-inch springform pan, cake pan, or cast-iron skillet with non-stick baking spray, or line the bottom with a round of parchment paper for easy removal.
Whisk the Dry Ingredients: In a medium mixing bowl, whisk together the all-purpose flour, unsweetened cocoa powder, cornstarch, baking soda, and salt until well combined and lump-free. Set aside.
Combine the Wet Ingredients & Color: In a large mixing bowl, vigorously whisk the melted and slightly cooled butter with the light brown sugar and granulated sugar until smooth. Whisk in the egg, egg yolk, vanilla extract, and red gel food coloring. Mix until the color is vibrant and the mixture is fully emulsified.
Form the Cookie Dough: Pour the dry ingredient mixture into the wet ingredients. Using a rubber spatula or wooden spoon, gently fold the mixture together just until a soft dough forms—be careful not to overmix, as this can make the cookie cake dense. Gently fold in the white chocolate chips.
Press and Bake: Press the cookie dough evenly into the prepared 9-inch pan. Scatter a handful of extra white chocolate chips on top and press them in lightly. Bake for 20 to 22 minutes. The edges should look set and slightly golden, but the center will still look soft and slightly underbaked.
Cool Completely :Remove the pan from the oven and place it on a wire rack. Let the cookie cake cool completely in the pan before attempting to frost or remove it, as it will continue to firm up as it cools.
Whip Up the Frosting: In a medium bowl, beat the softened cream cheese and butter together using a hand mixer on medium-high speed for about 2 minutes until completely smooth. Gradually add the powdered sugar one cup at a time, followed by the vanilla extract and a pinch of salt. Beat on high speed for another 1-2 minutes until light, fluffy, and pipeable.
Decorate and Serve: Transfer the cream cheese frosting to a piping bag fitted with a large open star tip (like a Wilton 1M). Pipe decorative swirls or a shell border around the edge of the cooled cookie cake. Slice and serve!