In a mixing bowl, beat together powdered sugar, butter, peppermint extract, and heavy cream until a thick dough forms.
Roll dough into small balls and flatten slightly into disc shapes.
Place discs on a parchment-lined tray and freeze for 15-20 minutes.
Melt chocolate chips with shortening in the microwave in 30-second intervals until smooth.
Dip frozen patties in melted chocolate and place on parchment paper to set.
Refrigerate until firm before serving.