Combine sugar, butter, cream, and peppermint until it is stiff like Play-Doh.
The paddle attachment on a stand mixer is perfect or this, starting low and increasing to medium speed.
Form dough into log-shape or long thin tube and wrap in cling wrap & twist ends cclosed.
Refrigerate dough log for at least an hour until chilled and firm.
you can cut a paper towel roll & sit your roll in side it so that the bottom doesn't get flat.
After it's chilled, unwrap the log and use a sharp knife to make patty slices about 1/4 inch thick (the thickness of an iPhone).
Melt chocolate & use a fork to drop patties into chocolate & flip. Then drain off excess.
Place peppermint patties on a sheet of wax paper to set at room temperature, which doesn't take long at all.
Store in an air-tight container, best in refrigerator.