Cream butter in a large mixing bowl; gradually add sugar, beating well. Add egg; beat well.
Combine flour, baking powder, and salt in a medium mixing bowl, mixing well. Add flour mixture, milk, and vanilla to creamed mixture, stirring well. Cover and chill thoroughly.
Roll to 1/8-inch thickness on a floured surface; cut with assorted symbol-shaped cutters. Place on ungreased cookie sheets. Bake at 375° for 6 to 8 minutes. Remove from cookie sheets, and cool on wire racks. Decorate as desired.