Combine peanut butter, shortening, brown sugar, milk and vanilla in large bowl. Beat at medium speed of electric mixer until well blended. Add egg. Beat just until blended.
Add the salt and baking soda and stir until mixed, then pour in the flour and mix on low until fully blended.
Drop by rounded measuring tablespoonfuls of dough 2-inches apart (or by large cookie scoop) onto a greased baking sheet. Flatten slightly in a crisscross pattern with tines of fork.
Bake one baking sheet at a time for 7 to 8 minutes, or until set and just beginning to brown. Cool 2 minutes on baking sheet. Remove cookies to cooling rack to cool completely.