Preheat oven to 350 F. In a medium bowl combine the flour and cocoa powder; set aside. In a large mixing bowl, beat together the butter with electric mixer on medium to high speed until blended, about 30 seconds. Add sugar, baking soda, baking powder, and salt. Beat until well combined. Add egg and vanilla; beat well. Gradually beat in flour mixture.
Shape dough into 1 inch balls. Place about 2 inches apart on ungreased cookie sheet. Press down center of each ball with your thumb. Drain maraschino cherries, reserve juice. Place a cherry into the center of each cookie.
For frosting combine the chocolate pieces and milk in a small saucepan. Heat and stir until chocolate is melted. Stir in 4 teaspoons cherry juice. Spoon about 1 teaspoon of the frosting over each cherry. Spread to cover cherry. Additional cherry juice may be needed to make spreading easier.
Bake about 10 minutes or until edges are firm. Cool on cookie sheet for 1 minute. Cool completely. Store in airtight tin for 3 days or freeze up to 3 months. Makes 48 cookies.