Preheat oven to 350 degrees F.
In a bowl, beat shortening and sugar until well mixed. Add eggs and beat until light and fluffy. Add sour cream and vanilla. Mix well. Add baking powder, baking soda, and salt. Add flour, 1 cup at a time until the mixture is very thick. Cover dough and chill in the refrigerator for several hours.
Roll out dough on floured surface to desired thickness and cut with cookie cutters. If desired, you may dust the tops with coarse sugar, before baking. Bake for 8 to 10 minutes. Cookies should just be lightly browned and soft when taken from the oven. Cool on wire rack and decorate.