In a mixing bowl, stir together the flour, baking powder, and salt.
In another bowl, beat the sugar and shortening with an electric mixer until light and fluffy. Add the eggs, one at a time, beating well after each addition.
Beat in vanilla and flour mixture until everything is well combined. Divide dough in half. Cover and chill for about 2 hours or until dough is easy to handle.
On a lightly floured surface or surface dusted with sifted powdered sugar, roll each portion of cookie dough to 1/8-inch thickness. Cut the rolled-out dough into desired shapes. Place 1 inch apart on ungreased cookie sheets.
Bake in a 375 degree F oven for 8 to 10 minutes or until edges are firm and bottoms are very lightly browned. Cool on a wire rack. Makes forty 2- to 3-inch cookies.
For a spiced cookie, add 1/4 to 1/2 teaspoon ground nutmeg to the flour mixture. You also can substitute 1/3 cup butter for 1/3 cup of the shortening for more butter flavor.