Preheat oven to 350°F (175°C). Lightly grease a 10-inch shallow cake pan or pie plate.
In a large bowl, beat softened unsalted butter, white sugar, and light brown sugar with a handheld mixer or stand mixer fitted with the paddle attachment. Mix on medium speed for 2–3 minutes, until light and fluffy.
Beat in the egg yolk and vanilla until smooth.
In a separate bowl, whisk together all-purpose flour, ½ teaspoon salt, and baking soda.
On low speed, slowly add the dry ingredients to the wet mixture. Mix until just combined. Stir in semisweet chocolate chips with a spatula. Do not overmix. Stop when the dough just comes together.
Spread the dough evenly into the prepared cake pan. Use a spatula or your fingertips to press it flat, making sure the edges are even.
Bake for 18–22 minutes, until edges are golden brown and the center looks just set but still soft. Bake time will vary slightly if using a deeper 9-inch cake pan or thinner pizza pan.
Let the cookie cake cool in the pan. Once cooled, frost with homemade buttercream. Use a piping bag for a decorative border or add a flat happy birthday topper.