Adjust oven racks to the upper and lower thirds of the oven, and preheat oven to 350 F degrees. Line two baking sheets with parchment paper and set aside.
In a small mixing bowl, add flour, cocoa powder, baking powder, baking soda, and salt. Whisk together and set aside. To another small bowl, add milk, espresso powder and vanilla and stir together until espresso powder dissolves. Set aside.
To the bowl of a stand mixer, add butter and sugar and beat until creamy and fluffy, about 1 minute. Add egg and beat until mixed in.
Add half of the flour mixture and mix until just combined. Add all the milk mixture, mix until combined. Add remaining flour mixture and mix until just combined. Increase speed slightly and mix until smooth, about 30 seconds to 1 minute.
Scoop batter onto prepared cookie sheets, about 2 inches apart. Bake, rotating pans halfway through, 12-14 minutes, until edges are set and the tops spring back slightly when touched. Cool on pans 3-5 minutes, then transfer to cooling racks to cool completely.