Combine shortening, peanut butter, brown sugar, milk and vanilla in large bowl. Beat with electric mixer at medium speed until well blended. Add egg. Beat just until blended.
Combine flour, salt and baking soda. Add to creamed mixture at low speed. Mix just until blended.
Drop by heaping tablespoonfuls (using a cookie scoop works great) 2 inches apart onto ungreased baking sheet. Flatten slightly in crisscross pattern with tines of fork.
Bake for 7 to 8 minutes, or until set and just beginning to brown. DO NOT OVERBAKE. Cool 2 minutes on baking sheet. Remove cookies to racks to cool completely.
When you bake these, start with a small batch and check them after 7 minutes. Mine are always perfect at 8 minutes. They will look a little underdone and puffy. Once you remove them from the oven and let them cool a bit, they will relax and settle.