In a mixing bowl, combine the powdered sugar, corn syrup, softened butter, and peppermint extract. Blend until fully combined and smooth.
Take small portions of the filling and roll into balls, then flatten each ball into a disc shape about 1/4 inch thick. Place them on a cookie sheet lined with wax paper.
Cover the cookie sheet with plastic wrap and refrigerate for about 30 minutes, or until the patties are firm.
Melt the dark chocolate with vegetable shortening in a double boiler or microwave, stirring until smooth.
Dip each chilled patty into the melted chocolate, ensuring they are fully coated. Tap off excess chocolate and return to the wax paper.
Let the dipped patties sit at room temperature or in the refrigerator until the chocolate is fully set.