In a medium mixing bowl, mix together the ingredients in the order listed. Start by creaming the shortening with the sugars, then add the vanilla; mix well.
Add the beaten eggs; mix well; set aside.
In a separate mixing bowl, thoroughly combine the flour, soda, and salt. Add the flour mixture, all at once, to the shortening-sugar mixture; mix well.
Add the oats and the butterscotch chips all at one time; mix well.
Grease (with vegetable shortening) a large 16-inch by 12-inch baking sheet.
Shape dough into golf ball-size balls, spacing 2 inches apart. Place 12 dough balls on the cookie sheet.
Bake at 350 degrees for 10 to 12 minutes. In my oven, the cookies are generally done baking in 11 minutes. Allow cookies to sit on the baking sheet 1 minute before removing them to a wire rack to cool completely.