Pulse half of cookies in a food processor 3 or 4 times or until crumb consistency. Add remaining cookies to crumbs in food processor, and pulse until crumb consistency. Cut cream cheese into 4 pieces; add to food processor, 1 piece at a time, processing well after each addition.
Roll cream cheese mixture into 1-inch balls. Push one chocolate-covered mint into the center of each ball; roll each ball smooth.
Microwave chocolate morsels and shortening in a glass bowl at HIGH for 90 seconds or until melted, stirring every 30 seconds.
Dip balls in melted chocolate mixture; place on wax paper to harden. Store in refrigerator.
Note: For testing purposes only, we used Oreo Sandwich Cookies and Junior Mints.