Mix molasses, shortening and brown sugar in a large bowl. Stir in flour, salt, baking soda, baking powder, and spices. Cover and refrigerate about 4 hours or until firm.
Preheat oven to 375 degrees F (190 degrees C).
Roll half of the dough at a time to 1/8 inch thickness or paper-thin on a floured cloth-covered surface.
Cut into 3 inch rounds with floured cutter.
Place about 1/2 inch apart on ungreased cookie sheet.
Bake 1/8 inch thick cookies about 8 minutes; paper-thin cookies about 5 minutes or until light brown. Immediately remove from cookie sheet. Cool completely.
Mix 1 cup confectioners' sugar, 1/2 teaspoon vanilla, and 1-2 tablespoons half-and-half until of spreading consistency.