Preheat oven to 350 degrees. Spray a 10-inch tart pan with cooking spray. In a large bowl, cream the butter and sugars until light and fluffy. Add egg, egg yolk, vanilla, food coloring, and vinegar and mix to combine.
Add flour, cocoa powder, corn starch, baking powder, and salt and mix until just combined. Stir in white chocolate chips. Pour into prepared pan, smoothing the top of the batter until even. Bake 30 minutes.
Meanwhile, make the frosting: In a medium bowl, beat cream cheese and butter until smooth. Gradually beat in powdered sugar, then vanilla and milk, until smooth and spreadable.
When cookie cake has completely cooled, spread frosting in a smooth layer on top. Sprinkle with colored sprinkles, if using. Keep refrigerated.
Cookie cake adapted from Just So Tasty. Frosting from Betty Crocker.