Whisk almonds with cocoa, baking powder and salt in a small bowl. Beat butter with brown sugar in a large bowl, using an electric mixer, until light and fluffy, about 3 min. Beat in egg and vanilla. Stir in cooled chocolate. Fold in almond mixture until combined. Cover bowl with plastic wrap and refrigerate until dough is firm enough to roll, about 10 min.
Position oven racks in top and bottom thirds of oven. Preheat oven to 350F. Line 2 baking sheets with parchment paper.
Place granulated and icing sugars in 2 separate small bowls. Scoop dough and roll into tbsp-sized balls. Coat with granulated sugar, then icing sugar. Place on prepared sheets 1 in. apart. Bake in top and bottom thirds of oven, switching and rotating sheets halfway through, until cookies crack, 12 to 14 min.
Remove sheets to a rack and leave for 2 min. Cookies will look undercooked but will continue to bake as they sit. Remove to a rack to cool completely.
Serve and enjoy!