In a large mixing bowl, beat butter with an electric mixer on medium to high for 30 seconds. Add granulated sugar, baking powder and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg, milk and vanilla until combined. Beat in cocoa powder and as much flour as you can with the mixer. Stir in any remaining flour. Divide dough in half. Cover and chill for 1 hour or until dough is easy to handle.

Preheat oven to 375°. On a lightly floured surface, roll one portion of the dough at a time to ⅛-inch thickness. Using a square- or rectangular-shape cutter (about 2½-inch square), cut out dough. Place cutouts 1 inch apart on ungreased cookie sheets.

Bake for 7 to 10 minutes or until edges are firm and bottoms are light brown. Transfer cookies to a wire rack and let cool.

Line cookie sheets with waxed paper; set aside. In a small saucepan, combine chocolate chips and shortening. Alternatively, melt chocolate chips and shortening in a double boiler, stirring until smooth. Cook and stir over low heat until melted. Dip tops of cookies into melted mixture. Place dipped cookies on prepared cookie sheets. Sprinkle with some of the crushed peppermint. Chill about 15 minutes or until set.