Preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.
In a bowl of a stand mixer fitted with the paddle attachment or using an electric hand mixer, cream together the butter and granulated sugar until light and creamy (about 2-3 minutes).
Scrape the bottom and sides of the bowl. Add the egg, mix on medium speed for 20 seconds, then add the egg yolk. Scrape down the sides, add vanilla extract, and mix on low until combined.
Add in the flour, Dutch-processed cocoa powder, baking soda, and salt. Mix on low just until the dry mixture disappears. Do not over mix.
Use a 3-tablespoon cookie scoop to form 12 cookie dough balls. Take two of the dough balls and roll them together into one big cookie ball. You should end up with 6 large cookies. Place them on the prepared baking sheets and gently flatten to about a little over ½ inch in thickness.
Bake in the preheated oven for 10-12 minutes. Let the cookies cool on the baking sheets for 10 minutes before transferring them to a cooling rack.
For cream cheese frosting
In the bowl of an electric mixer, combine the butter and cream cheese. Cream on medium speed for about two minutes. Scrape down the sides and bottom of the bowl. Beat again for 2 more minutes.
With the mixer on low speed, add the powdered sugar, followed by the, cake batter extract, vanilla, and salt. Beat on low just until mixed. Then turn the mixer to medium high speed and beat the mixture for 2-3 minutes.
With a rubber spatula, fold in the rainbow sprinkles.
Once the cookies are completely cooled, and no longer warm, frost the cookies.
With a plastic bag or a piping bag, cut a medium size hole and frost the top of the cookie and decorate with extra sprinkles.