Cream the butter and shortening with the sugar, then beat in eggs and vanilla. Combine flour, salt, and baking powder, then stir them into the creamed mixture to make a soft dough. Chill thoroughly.
Work with only a small amount of the cold dough at a time. Use lots of flour to roll dough. (I use a combination of flour and confectioners' sugar instead of plain flour. This gives the cookies a sweeter taste, and they do not taste like flour.) Roll about 1/8 inch thick, cut out cookie shapes, and use a metal spatula to transfer them to a lightly greased baking sheet. Bake at 375 degrees F for 7 to 10 minutes, or until lightly browned.
These cookies can be decorated a variety of ways. Sometimes I frost them after they are cool. Other times I use colored sugar sprinkled on them before baking. Most times, though, I use a mixture of egg yolks, a little water, and some food coloring and "paint" them before baking.