In a large mixing bowl, cream the shortening, 1 cup creamy peanut butter and white and brown sugars. Add vanilla and then eggs, one at a time. Beat well after each addition. In a small bowl, combine flour, baking soda and salt. Add slowly to creamy mixture.
Shape into 1 inch balls and place on an ungreased cookie sheet, 2 inches apart. Flatten balls with a fork.
Bake for 7-8 minutes depending on size (I tend to keep a close eye on them and remove them as soon as they start to get golden. This helps to make them chewy.) Cool on wire racks.
To Make the filling: Combine 1/2 cup creamy peanut butter, confectioners' sugar, vanilla extract, and milk in a small bowl adding enough milk to make for a creamy, frosting like texture. Spread frosting on one cookie and top off to make "sandwich".