Over medium/low heat, brown your butter in a pan. You want to give the butter a deep brown color, but be careful not to burn it. You need to whisk constantly - DO NOT WALK AWAY. Your nose will be a good indicator that it is done browning; it will smell nutty and toasted. Turn off the heat as soon as it's brown.
Allow the butter to cool. As it's cooling you should whisk in the heavy cream. It will become thick and creamy in texture.
While the mixture is cooling, whisk together your dry ingredients - baking soda, salt, and flour.
Once the butter has cooled, add your brown sugar, white sugar, and browned butter mixture to a stand mixer and mix until well combined.
Add your egg, egg yolk, and vanilla extract and mix until just combined.
Next, add your flour mixture and mix until just combined. No overmixing!
Add in the chocolate and again, mix until just combined.
Refrigerate the cookie dough overnight. I know, I know, the wait sucks, but it's important and worth it.
The next day preheat the oven to 350 degrees and line a cookie sheet with parchment paper. Bake 6 cookies at a time for 18ish mins.