Line a baking sheet with wax paper.
Place the sugar, butter, peppermint and vanilla extract, and cream in a blender. Blend on low speed until the ingredients are combined, then blend on medium-high until the mixture is creamy and well-incorporated, with no powdery bits.
Transfer into a bowl, then using a teaspoon or a melon baller, roll into small balls and place on the baking sheet. Flatten into patty shapes. Place in the refrigerator for 20 minutes.
In the meantime, melt the chocolate and vegetable shortening in a double boiler.
Using toothpicks, two forks, or tiny tongs, dip each patty into the melted chocolate, one by one. Place them back on the baking sheet, and return to the refrigerator to chill for at least two hours.
Store them in a covered container, refrigerated, for up to a month.