Preheat oven to 350 degrees.
In a mixing bowl combine flour and cocoa, set aside. In a large mixing bowl beat butter with an electric mixer on medium to high speed about 30 seconds or until softened. Add sugar, salt, baking powder and baking soda. Beat until well combined. Add egg and vanilla. Beat well. Gradually beat in the flour mixture.
Shape dough into 1-inch balls; place on ungreased baking sheet. Press down center of each ball with thumb. Drain maraschino cherries, reserving juice. Place a cherry in the center of each cookie.
In a small saucepan combine chocolate morsels and sweetened condensed milk; heat until chocolate is melted. Stir in teaspoons of the reserved cherry juice. Spoon about 1 teaspoon of frosting over each cherry, spreading to cover cherry. Frosting may be thinned with additional cherry juice, if necessary.
Bake in preheated oven for about 10 minutes or until done. Remove to wire rack; cool. Cover and store at room temperature up to 2 days. Makes 48 cookies.