In a medium saucepan, melt the unsalted butter over medium heat, stirring constantly for about 5-7 minutes until golden brown and nutty.

Combine the cooled brown butter with dark brown sugar and white sugar in a large mixing bowl. Beat in the egg and egg yolk, and add vanilla extract until smooth.

Whisk together the all-purpose flour, espresso powder, baking soda, and salt in a separate bowl.

Gradually add the dry mixture to the wet ingredients, stirring until just combined. Fold in the chopped dark chocolate.

Cover the dough with plastic wrap and refrigerate for at least 30 minutes or overnight.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop dough onto the sheet and bake for about 11-13 minutes.

Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.