Preheat oven to 350°. Prepare two large baking sheets with parchment paper.
In a light bottom pan, gently brown butter. Begin by melting on medium low heat, whisking often with a rubber spatula. Once butter is completely melted, reduce to low heat and continue stirring, for 5-6 minutes until butter turns a caramel color and has a nutty scent and solids just begin to separate. Remove from heat and let cool. You can help it cool faster by carefully transferring to a heat safe bowl. Let cool until just barely above room temperature.
Meanwhile, in a bowl, whisk together flour, salt and baking soda and set aside. Chop chocolate into pieces. They will be slightly uneven, some bigger than others, and that is what we are looking for. Set aside.
In a large mixing bowl, combine both sugars and vanilla with cooled brown butter. Use a hand whisk and whisk until glossy in appearance. Add egg and egg yolk, and whisk again until incorporated.
Add flour mixture to wet mixture and mix together with a rubber spatula, until just combined. Avoid over mixing. Then add chocolate pieces and stir until incorporated.
Quickly divide into 24 portions using cookie scoop or spoon. If dough becomes very warm or greasy, chill dough or entire sheet pan with dough balls, into the fridge for 30 minutes. If the dough becomes very warm, it will spread more creating a thinner cookie. Still delicious, but just not dense or thick.
Bake for 9-11 minutes until edges are just set. Let cookies cool on baking sheet for 5-10 minutes. During this time if you want to create that "chocolate pools" look, use a toothpick and ever so gently stir the top of the large chocolate chunks to create a smooth top. After cookies have cooled slightly, sprinkle with flaky salt. If you do this while the cookies are still very warm, the salt will dissolve.
Once cookies have cooled, move carefully to a cooling rack with a spatula. Enjoy warm or let cool completely before transferring to an air tight container. These cookies are best enjoyed warm, so warm them in the microwave for a few seconds or few minutes in the oven at 200°F.