Preheat the oven to 350°F and line a baking sheet with parchment paper. Set aside.
Brown the butter over medium heat, stirring constantly until it foams and turns golden brown with a nutty aroma. Remove from heat and allow to cool.
In a small bowl, combine the butter and sugars, and mix well. Add the egg yolk and vanilla extract, mixing until smooth and homogeneous.
Add the flour, salt, and baking soda. Mix until just combined with no streaks of flour remaining. Fold in the chocolate chips, but do not overmix.
Shape into 2 large or 2 medium cookies and place on the prepared baking sheet.
Bake for 11 minutes or until edges are golden brown, and centers are puffy but gooey.
Allow to cool before eating.