Cream the sugar and shortening together in a mixing bowl. Add the eggs, sour cream, and vanilla. Mix thoroughly. Add the flour, baking soda, and salt. Mix until well blended. Chill the dough for a minimum of 4 hours or overnight.
Preheat the oven to 375°.
Roll out the dough to 1/4-inch thickness on a floured surface or between layers or parchment paper and cut with cookie cutters. Bake on an ungreased cookie sheet for 8-10 minutes at 375°. Allow cookies to cool completely before frosting and decorating.