In a sturdy saucepan with a thick bottom, heat the butter over medium heat until it turns a lovely shade of golden brown. Stir continuously as the butter foams and releases a delightful nutty aroma. Remove the butter from the heat and let it cool completely before using.
In a large mixing bowl, combine the cooled brown butter with brown sugar and white sugar. Whisk the mixture until it's well blended. Add the egg, egg yolk, and vanilla, and mix thoroughly. Incorporate the flour, baking soda, and salt, folding until the ingredients are just combined. Carefully add the chocolate to the dough.
Chill the dough for at least an hour or, for best results, overnight.
When you're ready to bake, preheat the oven to 350°F and line two cookie sheets with parchment paper. Scoop out the cookie dough using a 1-ounce cookie scoop and place the dough balls about 2 inches apart on the prepared sheets. Bake for 12to 14 minutes, or until the edges turn a beautiful golden brown while the center remains delightfully gooey. Let the cookies cool before enjoying every bite!
