Preheat the oven to 350°F and line a baking sheet with parchment paper. Set aside.
In a large mixing bowl, add the softened butter and brown sugar. Cream together with a hand or stand mixer until light and fluffy, approximately 2–3 minutes.
Add the egg and vanilla extract, mixing until fully incorporated.
In a separate mixing bowl, whisk together the flour, cocoa powder, espresso powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a soft chocolate cookie dough forms.
Cover the cookie dough and refrigerate for approximately 30 minutes.
Using a tablespoon-sized cookie scoop, portion the dough into balls and place them on the prepared baking sheet, leaving approximately 2 inches between each cookie.
Using your thumb or the back of a rounded measuring spoon, gently press an indentation into the center of each cookie dough ball.
Bake for 10–12 minutes, or until the edges are set and the centers are slightly soft.
Immediately after removing the cookies from the oven, gently press the center of each cookie again using the back of a rounded measuring spoon to redefine the indentation.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack. Let cool completely.