Drain cherries, reserving 3 teaspoons juice. Cut cherries in half, and set aside.
Beat butter and sugar at medium speed with an electric mixer until creamy; add egg, vanilla, and 2 teaspoons reserved cherry juice, beating until blended. Combine flour and next 4 ingredients; gradually add flour mixture to butter mixture, beating until blended after each addition. Shape dough into 1-inch balls, and place on ungreased baking sheets. Press center of each ball with thumb, and place 1 cherry half in indentation.
Cook chocolate and milk in a small saucepan over low heat, stirring occasionally, until melted. Stir in remaining reserved cherry juice. Cool slightly. Spoon 1 teaspoon mixture over each cherry half.
Bake at 350° for 10 minutes. Freeze up to 3 months.