I love making these because they have that nearly magical we made these? quality of being the most excellent version of a thing that is already so beloved even in its store-bought state. Plus, if I can speak plainly, they're really inexpensive to make—especially if you already have the peppermint extract. If you don't already have the extract, it's worth buying because sometimes you might want to put a few drops in your hot chocolate or your hot fudge.
Sift the confectioners' sugar into the bowl of a standing electric mixer and beat in the shortening on medium speed. In a small bowl stir together the water, corn syrup, lemon juice, and extract, then beat it into the sugar mixture until combined.
Knead the mixture into a ball (it will be very stiff), then use the bottom of a glass pie plate and firm, even pressure to flatten the ball between sheets of wax paper into a 9-inch disk that's about 1/4 inch thick (if you try doing this with a rolling pin, you will be much more frustrated, I assure you). Place the disk (with the wax paper) on a cookie sheet and freeze until firm, around 15 minutes.
Place the frozen disk on a cutting surface, remove and reserve the wax paper, and cover the cookie sheet with parchment. Use a 1-inch round cutter to cut out patties, moving them to the parchment as they're cut. Gather the scraps into a ball, use the pie plate and wax paper to flatten it again, and cut more rounds until all of the filling is used. Freeze the rounds for 10 minutes.
Meanwhile, melt the chocolate in the top of a double boiler over barely simmering water. Coat the patties one at a time, balancing each on a fork and dipping (use another fork as needed to flip the patty in the chocolate), then shaking excess chocolate and scraping the bottom of the fork against the edge of the bowl before returning the coated patty to the parchment.
Make a ridged pattern one each patty by pressing a fork into the chocolate and lifting it straight up. Reheat the chocolate as necessary until all the patties are coated, then allow them to sit until set, about 1 hour. Optional: sprinkle patties, as they're coated, with the crushed mints.
Peppermint patties keep, layered between sheets of wax paper in an airtight container and chilled, 1 month. (Like they'll really last a month. I don't even know why I write these things.)