Sift, then measure flour. Into a large mixing bowl, sift flour again with baking soda, salt, and sugar.
Cut butter and shortening into dry ingredients, using a fork or pastry cutter, until it is fine as cornmeal.
In a separate medium bowl, whisk together milk, slightly beating eggs and vanilla.
Add the dry ingredients to the wet ingredients, beating until smooth.
Divide in half, then wrap dough tightly with wax paper and chill in refrigerator over night or for several hours.
Preheat oven to 425 degrees F.
Turn each dough half onto lightly floured board. Roll thin, with a rolling pin covered in flour, approximately 1/4" thick.
Cut dough with a large cookie cutter until you have cut approximately 4 dozen cookies. (Keep the dough cold by keeping the rolling and cutting process to a minimum, or else the dough will begin to warm and become sticky and hard to handle.)
Bake on an ungreased cookie sheet for 8 to 10 minutes.
Remove cookies to a cooling rack. They will crisp as they cool.
Eat plain or top with your favorite frosting recipe. These cookies are perfect for decorating for any party or holiday.