Preheat oven to 350°F. Line a couple sheet pans with parchment paper or silicone baking mats.
In a small bowl, whisk together the flour, cocoa, ground espresso, baking powder, and baking soda. Set aside.
Cut up 4 tablespoons (57 g) of the butter into small chunks and place in a large bowl. Place the remaining 10 tablespoons (142 g) of butter in a medium to large skillet or pot, preferably a light coloured one. Cook the butter over medium heat, stirring with a rubber spatula and swirling the pot often. The butter will foam as it cooks and then brown bits will start to form on the bottom of the pan. Scrape these brown bits from the bottom of the pan with your spatula as the butter cooks. It should begin to smell nutty. Once the butter looks golden brown and the brown bits are a deep golden brown, remove from the heat and pour into the large bowl with the remaining butter in it, scraping all of the brown bits into the bowl with the butter.
Stir until all the butter is melted. Stir in the granulated sugar, brown sugar, salt, and vanilla with a rubber spatula. Mix until combined. Whisk in the egg and the yolk until mixture is smooth and glossy, about 45 seconds. Let the batter sit for 2-3 minutes. Whisk again for 45 seconds.
Pour the flour mixture into the large bowl and mix with a spatula until combined and no flour remains visible. Add the chopped chocolate and stir to combine. You can also use your hands to knead the chocolate in.
Using a cookie scoop (2-3 Tablespoon in size - mine was 2½), scoop dough into round balls and place on prepared pans. You can fit 6-8 cookies on large sheet pans. Bake one pan at a time in the middle of the oven for the best results. Bake for 10-12 minutes or until cookies look puffed in the center and the edges are set. They should be quite soft and underdone, with slightly firmer edges. Let cool for 10 minutes on the sheet pan, then remove to cool on a wire rack.
Balls of cookie dough can be covered with plastic wrap and refrigerated for up to 48 hours before being baked. This may help develop the flavour (although I did not notice a difference) and can be a handy make-ahead option. Add a minute or two to baking time if refrigerating.