In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg and vanilla until combined. Beat or stir in the flour.
Divide dough in half. Shape each half of dough into a 6-inch-long roll. Wrap in plastic wrap or waxed paper. Chill in the refrigerator for 2 to 24 hours.
Using a sharp knife, cut dough into 1/4-inch-slices. (Reserve several dough slices for decorating. Tint some of dough with paste food coloring to form hats, hair, and earmuffs. Forcing dough through a garlic press will make "hair.") For each caroler's face, place a dough slice on an ungreased cookie sheet. If desired, use a straw to make an oval-shaped hole in the dough for the mouth. (It may be necessary to reform the mouth with the straw while baked cookie is still warm.) If desired, arrange small decorative candies for the eyes and nose and add other colored dough decorations before baking.*
Bake in a 375 degree F oven for 6 to 8 minutes or until edges are lightly browned. Carefully transfer cookies to a wire rack; cool. *(If desired, instead of adding candy decorations before baking, tint Powdered Sugar Icing and use a decorating bag fitted with a small plain or star tip to pipe icing on cooled cookies, giving each caroler eyes and a nose.) If desired, brush on red petal dust to make rosy cheeks. Makes about 40 cookies.
Powdered Sugar Icing
In a small mixing bowl stir together powdered sugar, vanilla, and enough milk to make icing of piping consistency. Tint with food coloring as desired.