In a large bowl, cream butter and sugar. Beat in the egg, cherry juice and vanilla. Combine the flour, cocoa, salt, baking powder and baking soda; gradually add to the creamed mixture.
Roll into 1-in. balls. Place 2-in. apart on ungreased baking sheets. Using the end of a wooden spoon handle, make an indentation in the center of each. Place a cherry half in each indentation.
In a small saucepan over low heat, melt chocolate chips with milk, stirring constantly. Remove from the heat; stir in cherry juice until blended. Spoon about 1 teaspoon over each cherry (frosting will spread over cookies during baking). Bake at 350° for 9-11 minutes or until set. Remove to wire racks to cool.