Preheat oven to 350 degrees. In a bowl, combine flour and cocoa powder. Set aside.
In a large mixing bowl, beat butter medium-to-high speed for 30 seconds. Beat in sugar, baking soda, baking powder, and 1/4 teaspoon salt. Beat in egg and vanilla. Gradually beat in flour mixture.
Shape dough into 1-inch balls. Place balls about 2 inches apart on an ungreased cookie sheet. Press down center of each ball with your thumb. Drain cherries, reserving juice. Place a cherry in the indent made by your thumb.
For frosting, in a microwave safe bowl combine chocolate pieces and the sweetened condensed milk. Heat until chocolate melts. Stir in 4 teaspoons of the reserved cherry juice.
Place fudge frosting in a sandwich ziploc bag, and snip the end off. Squeeze about 1 tsp. frosting over each cherry, spreading to cover cherry. Bake in preheated oven about 10 minutes or until edges are firm. Cool on cookie sheet for 1 minute. Transfer to wire racks, cool.