In a large bowl, cream the shortening, peanut butter and sugars until light and fluffy, about 4 minutes. Beat in eggs and vanilla. Combine the flour, baking soda and salt; add to creamed mixture and mix well.
Shape into 1-inch balls and place 2-inches apart on ungreased baking sheets. Flatten to ⅜-inch thickness with fork. Bake at 375 degrees for 7–8 minutes or until golden. Remove to wire racks to cool.
For filling, in a large bowl, beat the peanut butter, confectioners’ sugar, vanilla and enough milk to achieve spreading consistency. Spread on half of the cookies and top each with another cookie.