Preheat your oven to 350ºF.
Whisk together flour, Dutch cocoa powder, espresso powder, baking powder, and salt in a mixing bowl.
In the bowl of an electric mixer, beat butter and brown sugar until light and fluffy.
Add eggs one at a time and then add vanilla, mixing until well combined.
Pour in the melted chocolate and mix on low speed until incorporated.
Alternate adding the dry mixture and milk until just combined.
Transfer dough onto plastic wrap, cover, and chill for at least 2 hours.
Scoop tablespoonfuls of dough and roll into balls. If sticky, freeze briefly.
Roll each ball in granulated sugar and then powdered sugar.
Place cookies on a baking sheet, 2 inches apart, and bake for 12 to 15 minutes.
Let cool on a wire rack after baking.