In a large mixing bowl, combine condensed milk and peppermint extract. Beat in enough confectioners' sugar, a little at a time, to form a stiff dough that is no longer sticky. Form into 1 inch balls, then place on waxed paper and flatten with fingers to form patties. Let patties dry at room temperature two hours, turning once.
In a medium saucepan over low heat, melt chocolate with shortening, stirring often. Remove from heat. Dip patties, one at a time, into chocolate by laying them on the tines of a fork and lowering the fork into the liquid. Let cool on waxed paper until set.