Place the condensed milk, peppermint extract and vanilla extract in the bowl of a mixer. Add half of the powered sugar and beat with a mixer on low speed. Gradually add the remaining powdered sugar. Beat until a smooth dough forms.
Sprinkle powdered sugar over a piece of parchment paper. Place the peppermint dough on the parchment and sprinkle powdered sugar over the top. Roll into a 1/2 inch thick circle.
Using a 1 or 1 1/2 inch round cookie cutter, cut out circles from the dough. If your dough does not cut easily, simply place it in the freezer for a few minutes to firm up, then try again.
Transfer the peppermint rounds to a parchment lined baking sheet. Cover and freeze for 10-15 minutes.
Place the chocolate and shortening in a medium microwave safe bowl. Cook at 30 second intervals until melted, stirring occasionally.
Using a fork, dip the patties one by one in the chocolate, then place on a piece of parchment. Add sprinkles immediately. Let cool until set, then serve. Store in the refrigerator.