Thoroughly cream shortening, sugar, and vanilla.
Add egg; beat till light and fluffy. Stir in milk.
Sift together dry ingredients; blend into creamed mixture.
Divide dough in half. Chill 1 hour.
On lightly floured surface, roll to 1/8 inch thickness.* Cut desired shapes with cutters.
Bake on greased cookie sheet at 375 F about 6-8 minutes. Cool slightly, remove from pan. Makes 2 dozen. *Chill other half till ready to use.
Combine butter or margarine, salt, vanilla, and 1 c. of sugar. Add milk and remaining sugar. Add more sugar to thicken or milk to thin, if needed for spreading consistency.
Adapted from My friend, Beth