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 large mixing bowl combine the cooled brown butter, brown sugar, and white sugar. Beat until mixed together. Add in the egg, egg yolk, and vanilla extract. Mix well.
In separate bowl mix together the flour, espresso powder, salt and baking soda. Mix the dry ingredients into the wet until everything comes together. Fold in the chocolate chunks. Do not over mix.
Refrigerate the cookie dough for at least a half hour, or overnight.
When you are ready to bake the cookies, preheat the oven to 350°F and line a cookie sheet with parchment paper. Use a 1 ounce cookie scoop to scoop the cookie dough out into balls, placing them 2 inches apart on the prepared sheet. Bake for 11 minutes, or until the edges are just golden brown and the centers have puffed up but are still gooey.