Combine the powdered sugar, butter, peppermint extract, and heavy cream. Mix them with a stand mixer and paddle attachment or a hand mixer until the mixture comes together. You may need to use your hands to form the final sugar dough.
Over a long sheet of plastic wrap, form the peppermint dough into a long log, wrap tightly, and refrigerate for at least an hour.
When ready to make the candy, combine the chocolate with the butter in a bowl and microwave at half power for one minute at a time, stirring in between each minute, until the chocolate is melted.
Slice the peppermint dough into 1/4 inch thick rounds. Lay out a piece of wax paper to put your finished patty on.
I found three ways to successfully coat them in chocolate without having them melt in the bowl of chocolate. First, you can pipe the chocolate onto the wax paper, add the peppermint slice, pipe more chocolate on top, and then use a toothpick to spread if needed. Second, you can freeze the individual slices and then dip in the chocolate. Third, you can allow the slices to sit out until they dry a bit and then dip them.
While chocolate is still wet, sprinkle with crushed candy canes.
Store in airtight container or storage bag. Freezes well.
Makes about 2 dozen, serving size based off of one peppermint patty