Preheat the Oven: Preheat your oven to 370°F. Line a baking sheet with parchment paper.
In a medium saucepan, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter foams and turns a rich amber color with a nutty aroma, about 5-7 minutes. Watch closely to avoid burning. Once browned, immediately transfer the butter to a large heatproof bowl and let it cool to room temperature. I let my cool down for about 45 minutes!
Once the better has cooled down, combine the cooled brown butter, dark brown sugar, and white sugar. Use a whisk and whisk the ingredients until evenly combined and well incorporated. About 30-45 seconds.
Add the whole egg, whisk until evenly combined, then add the egg yolk, and whisk again until evenly combined. Add the vanilla extract and mix just until incorporated.
Add together the flour, baking soda, baking powder, salt, chocolate chip and switch to a rubber spatula to gently fold the dough until there are no more flour streaks. DO NOT OVER WORK THE DOUGH.
Scoop the dough using a 3-tablespoon-sized cookie scoop. For larger cookies, scoop two balls and press them together to form one larger ball, or simply use one scoop for a smaller cookie. Roll the dough into balls and place them on the prepared baking sheet. If making larger cookies, place 6 dough balls on the sheet, spacing them about 3 inches apart. For smaller cookies, you can place 9 dough balls on the sheet, spacing them accordingly.
Bake in the preheated oven for 13-15 minutes for larger cookies or 9-11 minutes for smaller cookies, until the edges are golden brown and the centers are still slightly soft. If desired, sprinkle a pinch of flaky salt on top of each cookie immediately after removing them from the oven.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.