In a bowl, cream the butter and brown sugar until light and fluffy.
Beat in egg and mix in the cooled chocolate.
In another bowl, sift the flour, cocoa powder, instant espresso coffee granules, baking powder, and salt together and with mixer on low add to the creamed butter mixture; then beat in the milk until combined. Cook's Note: Will make a sticky dough.
Flatten the dough into a disk, wrap in plastic wrap and chill in the freezer until firm, for about 45 minutes.
Preheat the oven to 350 degrees F.
Shape the dough into 1-inch balls and roll in the icing sugar 2 times, letting them sit in the icing sugar in between coatings and completely covered so no dough shows.
Place on parchment-lined cookie sheets 2-inches apart as the cookies will spread.
Bake until the cookies have spread and cracked, about 12 to 15 minutes.
Let cool on a cookie sheet.