1Cream butter; gradually add sugar, beating well at medium speed of an electric mixer. Add egg and vanilla; beat well.
2Combine flour and the next 3 ingredients; stir well. Gradually add to the creamed mixture, beating well.
3Shape the dough into 1 inch balls; place on ungreased cookie sheets. Press thumb into each ball of dough, leaving an indentation. Drain cherries, reserving 1 tablespoon plus 1 teaspoon juice. Press 1 cherry into indentation of each cookie.
4Combine the reserved cherry juice, chocolate morsels, and milk in a small saucepan. Cook over medium heat, stirring constantly, until the chocolate melts. Spread about 1 teaspoon frosting over each cherry.
5Bake at 350 degrees for 10-12 minutes. Let cool completely on the cookie sheets.