Melt the butter in a light-colored skillet over medium heat, swirling until golden brown specks form and it smells nutty.
Pour the browned butter into a large heatproof bowl.
Add both sugars and the salt to the hot butter, whisk to combine.
Let the mixture cool for 10 minutes.
Add the egg and egg yolk, whisk for 30 seconds.
Let stand for 3 minutes.
Whisk again for 30 seconds, let stand for 3 minutes.
Whisk a final time for 30 seconds, let stand for 3 minutes until mixture is thick and glossy.
Stir in the vanilla extract.
Fold in the flour and baking soda until a few streaks remain.
Add the chopped chocolate and fold until evenly distributed.
Cover and refrigerate the dough for at least 1 hour or overnight.
Preheat the oven to 375F and line two baking sheets with the parchment paper.
Scoop 2 tablespoon balls of dough onto the prepared sheets, spacing them a few inches apart.
Sprinkle each cookie with the flaky sea salt.
Bake for 10-12 minutes until edges are golden but centers remain soft.
Let cool on the baking sheets for 5 minutes before transferring to a wire rack.