Preheat oven to 350 degrees F. Add the butter, sugar and brown sugar to the bowl of a stand mixer fit with the paddle attachment. Or add the butter and sugars to a large bowl and use a hand-held electric mixer.
Mix on low until combined and then beat on medium-high speed for a couple of minutes until light and fluffy. Beat in the egg, and egg yolk, and vanilla extract until well combined. Be sure scrape down the sides of the bowl as you go.
In a separate small bowl, whisk together the dry ingredients - flour, espresso powder, baking powder, baking soda and salt.
Stop the mixer and add the flour mixture and the dark chocolate chips to the butter and egg mixture. Mix on low speed until a cohesive cookie dough forms, about 1 minute. Alternatively, you can use a rubber spatula or wooden spoon to stir and fold the dough together at this point.
Use a medium size cookie scoop (about 1 1/2 tablespoons capacity) to form 24 cookie dough balls. Place the cookies on baking sheets lined with Silpat baking mats or parchment paper (12 cookies per baking sheet).
Bake the cookies for 10 - 11 minutes. I rotate the pans front to back and top rack to bottom rack halfway through baking time.
The cookies should look a bit underdone when you take them out of the oven. They will set up as they cool.
Allow the cookies to cool on the baking sheets for 15 minutes, or until they've firmed up. Remove the cookies to a wire rack and allow them to cool to room temperature.
Cookies are best eaten within a day or two. If you'd like to freeze the cookies, layer them into an airtight container, separating the layers by sheets of wax paper. They will stay fresh in the freezer for up to one month.