Preheat oven to 350°F and line a 9x13-inch baking pan with parchment paper so there's excess on either side (this will make it easier to lift the baked brownies out for slicing later).
In a bowl, combine melted butter with brown sugar and granulated sugar with a spatula or wooden spoon. Add egg and yolk one at a time, mixing for 30-60 seconds after each. Batter will thicken and lighten in color. Stir in vanilla extract.
Add flour, baking soda and salt to the bowl and stir to combine. It will take a minute for the dough to come together as you stir it, but it will! Stir in chocolate chips, reserving a small handful to add to the cookie dough tops before baking.
Melt butter and chocolate chips in a saucepan over low heat. Remove from heat and stir in sugar, then the eggs one at a time. Stir in vanilla extract.
Add flour and salt and mix by hand until no streaks of flour remain.
Spread brownie batter into an even layer into the prepared baking pan.
Scoop or portion cookie dough into roughly rounded tablespoons and press slightly into the brownie batter. Add reserved chocolate chips to the top of the cookie dough and brownies.
Bake for 35-45 minutes, until cookies are golden brown and brownies are set in the middle (Baking time varies based on your oven, and your preferred brownie doneness. Shorter time will yield soft fudgy brownies with chewy cookie bites, and baking for longer yields firmer brownies with cakier cookie bites).
Let brownies cool completely for a few hours at room temperature, or for about 30 minutes in the fridge, before slicing.