Preheat your oven to 350 °F (175 °C). Line two baking sheets with parchment paper.
Brown the butter: cut butter into chunks and melt over medium in a light-colored skillet, stirring constantly until foam subsides and solids turn golden (5–8 minutes). Transfer immediately to a large bowl.
Stir in both sugars until the mixture cools just to lukewarm, about 5 minutes. Whisk in eggs, yolk, and vanilla until smooth and pale.
Fold in flour, baking powder, baking soda, and salt until just streaks of flour remain. Gently mix in chocolate chips.
Let dough rest 10 minutes (this hydrates the flour and limits spread). Meanwhile, line up cookie sheets.
Portion dough into 2-tablespoon mounds (a #40 scoop works well). Space them 2 inches apart.
Bake for 10–11 minutes until edges set but centers stay soft. Remove from oven and, if using, top each cookie with a few flaky salt crystals.
Cool on sheets for 5 minutes before transferring to a rack to finish cooling.