In a large bowl, beat the sweetened condensed milk and the peppermint extract on low speed, using a hand mixer, until thoroughly mixed, about 2 minutes.
Allow the disks to dry for approximately 3 hours. Flip the disks over and let dry an additional hour. They should be dry enough for you to handle them and they will not bend.
In a medium-sized, microwave-safe bowl, melt chocolate wafers and the vegetable shortening in the microwave using 20 sec increments at half power. This should only take a few minutes.