Preheat your oven to 325°F. Grease lightly and line a 9-inch round cake pan with unbleached parchment paper and set it aside.

In a large bowl with a handheld mixer or a stand mixer with the paddle attachment, place the butter, granulated sugar, brown sugar, and vanilla, and beat until creamy (about 2 minutes). Stop beating before the mixture becomes truly light and fluffy.

Add the egg and yolks, baking soda, and salt, and beat again until well-combined (about another minute).

Add the chocolate chips to the flour blend, toss the chips in the flour to coat, and then add them both to the bowl.

Mix until combined. The dough will be thick but soft.

Scrape the dough into the prepared cake pan, and use a moistened offset or other spatula to spread it into an even layer. Run the spatula from the center to the edges for more batter along the perimeter to create a crusty edge on the baked cake.

Bake, rotating once, for about 30 minutes or until lightly golden brown all over and a toothpick inserted in the center comes out mostly clean (not wet). If the top is very brown but the cake is not fully baked, reduce the oven temperature to 300°F, tent the pan with foil, and continue to bake for about another 5 minutes.

Remove from the oven and place the cake, still in the pan, on a wire rack to cool completely at room temperature.

Place the cooled cake in the pan, uncovered, in the refrigerator until firm (about 30 minutes).

To remove the cake from the pan, turn the pan over onto the palm of one hand, and remove the pan. Reinvert the cake onto a serving platter. You can also serve the cake right from the pan.

In the clean bowl of your stand mixer fitted with the paddle attachment or a clean large bowl with a handheld mixer, place the butter and beat on medium speed until light and fluffy (about 3 minutes).

Add the milk and vanilla, and turn the speed to mix until well-combined.

Add the salt and about 2 cups of confectioners’ sugar. Mix slowly until the sugar is incorporated, then turn the mixer up to high and beat until it becomes uniformly thick.

Add the rest of the confectioners’ sugar if necessary to thicken the frosting.

Transfer the white frosting to a piping bag fitted with a large open star tip or a sealed ziptop bag with the corner snipped off.

Use the white frosting to make the stars or dollops around the border of the cookie cake, just beyond the crust.

Allow the frosting to set at room temperature until it hardens a bit. Slice into wedges and serve.