Preheat the oven to 350°. Line 2 baking sheets with parchment paper.
In an electric mixer, beat together the butter, sugar, espresso powder if using, baking powder, baking soda, salt and vanilla until smooth. Clean the sides of the bowl with a spatula.
Add the egg, beating and scraping the sides again.
Add the cocoa and stir with a wooden spoon.
Alternating with the milk, add the flour to the batter in ⅓ cup increments.
Scrape down the sides of the bowl and mix again with mixer to soften and incorporate everything fully.
Using a medium sized cookie scoop or a ¼ cup measure, drop the dough 3 across the cookie sheet so that you'll have enough room for them to spread.
Bake for 9-10 minutes until the cookies are set and firm to the touch. Remove them from the oven and after 2-3 minutes, use a spatula to remove them to a wire rack to completely cool.