In a large mixing bowl, stir together the sweetened condensed milk and peppermint extract until fully blended. Gradually incorporate the powdered sugar, beating continuously to form a thick mixture. Turn the mixture out onto a flat surface dusted with powdered sugar and knead until a stiff dough forms; incorporate additional sugar if the texture remains sticky. Roll the dough to a uniform thickness of 1/4 inch and use a small circular cutter (approximately 1¼ to 1½ inches in diameter) to shape the patties—avoid larger sizes as they are prone to breaking during dipping. Arrange the cut patties on a flat surface and allow them to dry thoroughly for a minimum of two hours per side to achieve the necessary firmness. In a double boiler, melt the chocolate chips together with the shortening, using one tablespoon of shortening per six ounces of chocolate, and stir constantly until the mixture becomes smooth. Maintain the melted chocolate at a warm temperature suitable for dipping. To coat the patties, position one on a long, three-pronged fork and submerge it in the chocolate—ideally at a depth of no more than 1½ inches—flipping to ensure even coverage. Remove the patty by lifting it with the fork beneath, gently shake to remove excess chocolate, and transfer to waxed paper. Allow the patties to set until fully hardened.