In a medium saucepan, melt butter over medium heat, then bring to boil.
Once it starts boiling, swirl the pan constantly until the butter passes the foamy phase and becomes a deep amber color.
Remove from heat and pour into a large mixing bowl to cool for about 20 minutes.
While butter is cooling, preheat oven to 350° F. Line a baking sheet with parchment paper and set aside.
In a large bowl, using an electric hand mixer, mix together (cooled) browned butter, brown sugar, and granulated sugar until well combined.
Add in egg, egg yolk and vanilla extract. Mix until lighter in color, about 2 minutes.
Mix in the flour, baking soda, and salt. Using a rubber spatula, scrape the sides of the bowl and the bottom really well to ensure a smooth, well combined batter.
Hand stir the chocolate chips into the batter and let it sit 20 minutes to let the flour soak into the rest of the batter.*
Scoop cookie dough onto prepared pans 2 inches apart, using a two tablespoon cookie scoop.
Bake 8-9 minutes, rotating sheets half way through baking. When you pull your cookies out of the oven, they will looked cooked around the edges and undercooked in the center. DO NOT OVER BAKE!
Carefully place a few chocolate chips on top of each cookie immediately after removing from oven, pressing into the warm soft cookie just slightly.
Leave the cookies on the hot baking pans for 5-7 minutes or until you can remove them without falling apart. Place onto cooling racks and cool to room temperature before storing in airtight containers.