In a medium saucepan, brown butter over medium heat. Stir constantly to prevent burning. In 6-10 minutes the butter boils will develop a nutty aroma and brown solids will settle at the bottom.
Immediately pour the browned butter into a liquid measuring cup to stop the cooking. Add ice-cold water until the total volume reaches 1 cup. Refrigerate for 10–15 minutes, or until the butter reaches room temperature.
Dry ingredients: Sift together the flour, salt, and baking soda in a medium bowl. Set aside.
Wet ingredients: In a large mixing bowl or stand mixer, combine the brown sugar, white sugar, vanilla extract, coffee powder, and cooled butter. Beat with an electric mixer until light and fluffy, about 2 minutes. Beat in the whole egg and the egg yolk until fully incorporated.
Mix in the dry mixture to the wet ingredients in thirds. Fold in the chocolate.
Transfer the dough onto plastic wrap and shape it into a log. Wrap tightly and refrigerate for at least 1 hour, preferably overnight.
Slice the dough log into 1.4 oz pieces. Place them evenly on the baking sheet with parchment paper. DO NOT roll the dough balls.
Bake for 12.5 minutes at 350°F (175°C).
Remove cookies from the baking sheet IMMEDIATELY. Sprinkle sea salt on top if desired. Let them cool for a few minutes before serving.
