Combine butter and sugar in large bowl. Beat at medium speed, scraping bowl often, until creamy. Add milk, egg and vanilla. Continue beating until well mixed. Add flour and baking powder; beat at low speed until well mixed. Cover; refrigerate 1 hour or until firm.
Heat oven to 375°F. Roll out dough on lightly floured surface, one-half at a time (keeping remaining dough refrigerated), to 1/8-inch thickness. Cut with assorted 2-inch cookie cutters. Place 1 inch apart onto ungreased cookie sheets. Bake 5-7 minutes or until edges are lightly browned. Cool completely. Frost and decorate cooled cookies as desired.
Roll dough to 1/8-inch thickness. Cut with 3-inch cookie cutters. Bake as directed above. 2 1/2 dozen.