Create the Peppermint Filling. In a mixing bowl, combine the powdered sugar, softened butter, peppermint extract, and corn syrup. Start with 1 tablespoon of water and mix everything together until you have a soft, pliable dough. If it's too dry, add a bit more water, a teaspoon at a time.
Create the Patties and Freeze. Roll the peppermint dough into a log, about 1-inch in diameter. Then, slice it into individual patties, around 1/4-inch thick. Place them on a parchment paper-lined tray and freeze for about 30 minutes.
Make the Chocolate Shell. In a microwave-safe bowl, melt the chocolate and vegetable shortening (if using) in 30-second intervals, stirring between each interval until smooth.
Assemble the Peppermint Patties. Using a fork or dipping tool, submerge each frozen peppermint patty into the melted chocolate, ensuring it's fully coated. Shake off any excess chocolate and place the coated patty back onto the parchment paper.
Allow to Set. Let the patties sit until the chocolate hardens. You can speed up the process by placing them in the refrigerator for about 15-20 minutes.
Serve and Enjoy! Once the chocolate has set, your homemade peppermint patties are ready to enjoy! Store them in an airtight container in a cool place.