Heat oven to 350°F. Remove wrappers from chocolates.
Stir together cookie mix and flour; add butter and egg. Stir until dough forms. Set aside 1/4 cup small chocolate chips. Stir remaining chips into dough. (Dough is stiff; chips may need to be worked in with hands.)
Mold a tablespoon dough around each chocolate piece, covering completely. Shape into balls; place on ungreased cookie sheet.
Bake 9 to 11 minutes or until cookie is set. Cool slightly; remove from cookie sheet to wire rack. Cool completely.
Place remaining 1/4 cup chips and shortening in heavy-duty resealable plastic food storage bag. Microwave at MEDIUM (50%) 30 seconds; stir. If necessary, microwave at MEDIUM an additional 10 seconds at a time, kneading after each heating, until chocolate is melted and mixture is smooth. Cut off corner of bag about 1/8 inch from point. Drizzle over cookies.