Brown the butter over medium heat, stirring constantly until the butter begins to foam and turns a golden brown, emitting a nutty aroma. Take butter off the heat and allow to cool.
In a small mixing bowl combine the butter and the sugars and mix well. Add the egg yolk, and vanilla extract and mix until smooth and homogenous.
Add the flour, salt and baking soda. Mix until just combined and no streaks of flour remain. Last, fold in the chocolate. Do not over mix.
Shape into 2 huge cookies or 2 medium size cookies and place on your prepared cookie sheet.
Bake for 11 minutes*, or until the edges are just golden brown and the centers have puffed up but are still gooey.