Melt the butter in a small saucepan over medium-low heat, stirring and scraping the pan every 10–15 seconds. The butter will melt, foam, then turn golden brown with nutty aroma and small brown bits (about 5–7 minutes). Remove from heat and let cool slightly.
In a large bowl, mix the brown butter with brown sugar and granulated sugar. Add the egg, extra yolk, and vanilla and mix well.
Fold in the flour, baking soda, and salt until just combined,do not overmix. The dough should be soft, not sticky. Gently fold in the chocolate chips.
Cover and chill for at least 1 hour (or overnight).
