In a stand mixer, combine sweetened condensed milk, peppermint extract, and vanilla extract. Mix on medium speed for about 1-2 minutes until well blended and smooth.

Gradually add powdered sugar, about a cup at a time, while the mixer is on low speed. Continue to mix for about 3-5 minutes until a pliable dough forms.

Sprinkle a generous amount of powdered sugar on a clean surface or parchment paper. Turn out the dough onto the sugared surface and knead it gently.

Roll the dough out with a rolling pin to a thickness of about ½ inch.

Cut out circles from the rolled dough using a cookie cutter or round glass.

Place the baking sheet with the cut circles into the freezer and freeze for about 15 minutes.

In a microwave-safe bowl, break up dark chocolate into smaller pieces and melt in the microwave in 30-second increments.

Dip the chilled peppermint patties into the melted chocolate, ensuring they are fully coated.

Place the baking sheet back in the refrigerator for about 20 minutes to allow the chocolate to set completely.

After the chocolate has set, serve the peppermint patties or store them in an airtight container.