- Mix thoroughly shortening, butter, egg, and sugar. Stir in milk. Sift dry ingredients together, then stir into wet ingredients.
- Chill dough at least one hour. Preheat oven to 400 degrees. Drop rounded teaspoonfuls about 2" apart on lightly greased (or parchment covered) cookie sheets. Bake until almost no imprint remains when lightly touched, about 8-10 minutes. Frost when cool.
- Melt butter until golden brown. Blend in sifted confectioners sugar and vanilla. Stir in hot water to make a good spreading consistency.