Heat oven to 350°F. Grease baking sheets with shortening. Place sheets of foil on counter for cooling cookies.
For cookies, combine shortening, brown sugar, milk, egg, and vanilla in a large bowl. Beat at medium speed with electric mixer until well blended.
Combine oats, flour, baking soda, and salt.
Mix into the creamed mixture at low speed until blended.
Place rounded measuring tablespoonfuls of dough 2 inches apart onto prepared baking sheets.
Bake one sheet at a time at 350° for 10-12 minutes, or until lightly browned. Do not overbake. Cool 2 minutes on baking sheet. Remove cookies to foil or cooling rack to cool completely.
For frosting, combine powdered sugar, shortening, and vanilla in a bowl. Beat at low speed, adding enough milk for good spreading consistency. Spread on bottoms of half the cookies. Top with remaining cookies. I recommend refrigerating these cookies when saving for later. Don't forget a glass of ice cold milk!
Until next week,