Preheat the oven to 350°F (175°C). Grease or line a 9-inch round cake pan with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt until well combined.
In a large bowl, mix the melted butter, light brown sugar, and granulated sugar until smooth and creamy.
Add the egg, egg yolk, and vanilla extract to the butter and sugar mixture. Beat until light and creamy, about 2 minutes.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Fold in the semisweet chocolate chips evenly throughout the dough.
Spread the cookie dough evenly into the prepared cake pan, smoothing the top with a spatula.
Bake in the preheated oven for 22 to 25 minutes, or until the edges are golden brown and the center is set but still soft. A toothpick inserted near the center should come out with a few moist crumbs.
Remove the cookie cake from the oven and allow it to cool in the pan on a wire rack for at least 20 minutes before slicing and serving.