Cube the butter and place in a light-colored skillet. (Light colored helps you determine when the butter begins browning.) Melt the butter over medium heat, stirring constantly. Once melted, the butter will begin to foam. Keep stirring. After 5-8 minutes, the butter will begin browning; you’ll notice lightly browned specks begin to form at the bottom of the pan and you'll begin to smell a nutty aroma. Once browned, immediately remove from heat, pour into a large heat-proof mixing bowl, and set aside.
In a separate large bowl, sift together the flour and baking soda. Add the coarse sea salt to the sifted mixture and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or using an electric hand mixer, cream together the sugars, salt, vanilla, espresso powder, & cooled brown butter until combined and fluffy, about 5 minutes. Add the egg and egg yolk and mix until incorporated.
Add the flour mixture, about ¼ of the mixture at a time, and mix between additions until just incorporated. Fold the chocolate chips and chunks into the dough
Using a medium cookie scoop, drop the dough on a parchment paper-lined baking sheet. Cover with plastic wrap and place in the fridge.*
Bake in a 350°F preheated oven for 13-15 minutes. Allow the cookies to cool for 5 minutes on the baking sheet, then transfer them to a wire rack to cool completely. If desired, sprinkle a small amount of flaked sea salt on top of the cookies as they are cooling.
Chill the dough for at least one hour though overnight is best. For those times that I have no self control, I will often bake half of the cookies after chilling the dough for an hour, and then bake the other half the following day.