Step 1

Make the cookie base: Place 1 stick unsalted butter in the bowl of a stand mixer fitted with the paddle attachment for the cookie base (or in a large bowl if using an electric hand mixer) and 4 tablespoons unsalted butter for the frosting on the counter. Let sit out at room temperature until softened, about 45 minutes.

Step 2

Arrange a rack in the middle of the oven and heat the oven to 350°F. Coat 1 (9-inch) round cake pan with cooking spray, then line the bottom with a round of parchment paper.

Step 3

Add 2/3 cup packed light brown sugar and 1/3 cup granulated sugar to the bowl of butter. Beat on medium-high speed until light and fluffy, 2 to 3 minutes. Beat in 2 large eggs one at a time, waiting until the first one is fully incorporated before beating in the second. Add 1 1/2 teaspoons vanilla extract and beat just until combined, 1 minute.

Step 4

Turn the mixer off. Add 2 cups all-purpose flour, 1 teaspoon kosher salt, and 3/4 teaspoon baking soda. Beat on low speed until incorporated, 1 to 2 minutes. Stir in 1 cup of the semi-sweet chocolate chips by hand.

Step 5

Transfer the dough to the baking pan and press into an even layer with your hands. (If the dough is too sticky, lightly coat your hands with cooking spray.) Sprinkle the remaining 2 tablespoons chocolate chips on top.

Step 6

Bake until the top is lightly browned and no longer shiny, 20 to 25 minutes. Place the pan on a wire rack and let the cookie cool completely in the pan.

Step 7

Make the frosting: Place the 4 tablespoons room temperature unsalted butter in the clean bowl of a stand mixer fitted with a whisk attachment. (Alternatively, use an electric hand mixer and large bowl.) Add 2 tablespoons unsweetened cocoa powder, 1 tablespoon plus 1 teaspoon milk, and 1/4 teaspoon vanilla extract. Beat on low speed until smooth, 2 to 3 minutes. Turn the mixer off.

Step 8

Add 1 cup powdered sugar and mix on low speed until combined, 1 to 2 minutes. Increase the speed to high and beat until the frosting is light, fluffy, and doubled in volume, scraping down the sides of the bowl down halfway through, 1 to 2 minutes total. Transfer the frosting into a piping bag fitted with a star tip or a zip-top bag and set aside.

Step 9

Assemble the cookie cake: Remove the cookie from the pan and discard the parchment. Place the cookie on a cake stand or serving plate. Pipe small, decorative mounds of the frosting around the edge of the cookie. Sprinkle the frosting mounds and cookie with 2 tablespoons rainbow sprinkles.