Beat butter and sugar in large mixing bowl; add egg, milk and vanilla, blending thoroughly. Stir together flour, cocoa, baking soda and salt. Add to butter mixture, blending well. Refrigerate dough about 1 hour or until firm enough to handle. (Dough will be a little soft.)
Heat oven to 350°F. Lightly grease cookie sheet or line with parchment paper. Remove wrappers from peppermint patties.
Roll dough into 1-1/4 inch balls. For each cookie flatten ball slightly; press peppermint pattie into dough. Mold dough around pattie so that it is completely covered. Place on prepared cookie sheet. Using knife edge press star design into surface of each cookie; sprinkle with decorator's sugar.
Bake 12 to 14 minutes or until cookie is set; sprinkle with additional sugar, if desired. Cool slightly; remove from cookie sheet to wire rack. Cool completely. About 2 dozen cookies.