In a large bowl, cream together the shortening, white sugar and brown sugar until smooth. Beat in the eggs one at a time, then stir in the orange zest, molasses and vanilla. Combine the flour, baking soda and salt; stir into the molasses mixture until well blended. Mix in oats.
Divide the dough into halves, and shape into long logs about 2 inches in diameter. Wrap in waxed paper, and refrigerate for at least 8 hours or overnight.
Preheat the oven to 350 degrees F (175 degrees C). Slice chilled dough into rounds about 1/4 inch thick. Place 2 inches apart onto ungreased cookie sheets.
Bake for 11 to 13 minutes in the preheated oven, until the bottoms are lightly browned. Cool on the baking pan for a minute before removing to wire racks to cool completely.
