In a large bowl or stand mixer, cream together shortening and sugar until light and fluffy.
Add eggs and vanilla and beat until well blended and smooth.
Sift together flour, salt, baking powder, and baking soda and slowly add to creamed mixture.
Chill dough for at least 3 hours.
Preheat oven to 375 F.
Roll dough to 1/8 to 1/4 inch thickness on a lightly floured board.
Flour or spray cutter with cooking spray (especially if you're using detailed cutter like these).
Place cookies on a parchment lined baking sheet and bake for 8-10 minutes.
Let cool completely before icing.