In a large mixing bowl beat shortening and 1/2 cup peanut butter with an electric mixer on medium to high speed for 30 seconds. Add 1/2 cup granulated sugar, brown sugar, and baking soda. Beat until combined, scraping sides of bowl occasionally. Beat in egg and milk until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Divide dough in half. Cover and chill for 1 to 2 hours or until dough is easy to handle.
Bake about 8 minutes or until light brown. Transfer cookies to a wire rack; cool.
For filling, in a medium mixing bowl beat cream cheese, 1/2 cup peanut butter, 3 tablespoons granulated sugar, and vanilla on medium speed until smooth.
Spread about 1 tablespoon of the filling on bottoms of half of the cookies. Top with the remaining cookies, bottom sides down. Roll edges of sandwich cookies in chopped peanuts to coat. Store, covered, in the refrigerator.