In a small bowl stir together flour, cocoa powder, baking powder, and salt; set aside. In a medium mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and brown sugar. Beat until combined, scraping sides of the bowl occasionally. Beat in egg and espresso powder until combined. Beat in as much of the flour mixture as you can with the mixer. Using a wooden spoon, stir in any remaining flour mixture.
Divide dough in half. Shape each half into a 6-inch roll. Wrap each roll in plastic wrap or waxed paper. Chill for at least 2 hours or until dough is firm enough to slice.
Preheat oven to 350 degrees F. Line a large cookie sheet with parchment paper. Cut rolls into 1/3-inch slices (18 slices per roll). Place slices 1 inch apart on the prepared cookie sheet. Bake about 8 minutes or until set. Transfer cookies to wire racks; cool.
For icing, in a small bowl combine powdered sugar and coconut extract. Stir in enough of the milk to reach drizzling consistency. Drizzle cookies with icing. Sprinkle with coconut.