Brown the butter in a light-colored medium-sized pot, place butter inside and cook on low medium heat. No need to stir consistently, just allow the butter to melt and begin cooking.
About halfway through the butter will begin to foam up a bit, but you only need to take your rubber spatula and stir it to bring it back down a bit. Continue to cook on the same heat, and about 6 to 7 minutes in you will begin to see light foaming on the top.
You will notice along the edges browning, and if you stir the butter there will be small browned pieces at the bottom (milk solids). Begin stirring at this point until the color is a light to medium color and you smell the nutty flavor of the butter.
Remove from heat and pour into a medium heat-safe bowl. Allow to cool (solidify slightly) before moving to the next step.
Combine flour, espresso powder, baking soda, and fine sea salt in a small bowl. Whisk well and set aside.
Add sugars and vanilla to the butter and whisk well until the mixture is lighter in color.
Add egg and whisk until well combined.
Add dry ingredients to wet ingredients. Use a whisk or rubber spatula to combine.
Add ¾ part of the chopped chocolate chunks and fold them into dough with a rubber spatula.
Cover with plastic wrap and refrigerate for a minimum of 1 hour, but no more than 2 hours.
Preheat oven to 375 F. Remove from refrigerator and use a large cookie scoop (3 tablespoons) to scoop dough. Press firmly into the scoop before removing. Place on a baking sheet fitted with parchment paper at least 3" apart.
Roll or spread the remaining chopped chocolate on top of the cookies.
Bake for 12 minutes, or until edges are browned. Remove from oven and place on cooling rack to cool.