1. Line 8- or 9-inch square pan with foil; butter foil.
2. Cook butter, peanut butter and milk in large saucepan over very low heat, stirring constantly, until mixture is melted. With wooden spoon gradually beat in powdered sugar and vanilla. Remove from heat; pour into prepared pan. Cool completely. (Mixture will appear dry, but softens when rolled into balls.)
3. Line two trays with wax paper. Spread chopped peanuts on one tray; set aside. Roll peanut butter mixture into 3/4-inch balls and place on second tray. If necessary, refrigerate peanut butter balls until firm enough to handle easily for coating.
4. Place chocolate chips and shortening in medium microwave-safe bowl. Microwave at MEDIUM (50%) 1 minute; stir. If necessary, microwave at MEDIUM an additional 15 seconds at a time, stirring after each heating, until chips are melted and mixture is smooth when stirred. Cool slightly.
5. Dip peanut butter balls completely into chocolate mixture, one at a time, with fork. Gently tap fork on side of bowl to remove excess chocolate. Immediately roll in chopped peanuts; gently reshape if necessary. Place candy balls into small paper candy cups or return to wax paper-lined tray. Refrigerate until firm, about 20 minutes. Store in cool, dry place. About 5 dozen candies.
Recipe can be doubled.