Heat oven to 375. In large bowl, beat sugar, 1 cup butter and the vanilla with electric mixer on medium speed until fluffy. Beat in egg yolk until smooth. Beat in flour and cocoa.
Shape dough by rounded teaspoonfuls into 1 inch balls. On ungreased cookie sheet, place balls 1 inch apart. With inxes finger or thumb, make indentation in center of each ball.
Bake 7-9 minutes or until set. Immediately remove from cookie sheet to wire rack. Cool completely, about 30 minutes.
In small bowl, beat 1/4 cup butter and the powdered sugar on low speed until smooth. Beat in milk, peppermint extract and enough food color for desired color. Spoon about 1/2 t. filling into each cookie.
Melt the chocolate chips and shortening, and drizzle over the tops of each cookie.