Step 1: Prepare the Dough

1. In the bowl of a stand mixer, combine ¾ cup sweetened condensed milk, 1 ¼ teaspoons peppermint extract, and ⅛ teaspoon vanilla extract.
2. Turn the mixer to low and gradually add 2 cups of powdered sugar. Continue adding the remaining 2 cups bit by bit until the mixture forms a smooth dough.

Step 2: Knead and Roll the Dough

1. Sprinkle about 3 tablespoons of powdered sugar onto a piece of parchment paper to prevent sticking.
2. Place the dough onto the powdered surface and knead it a few times to ensure everything is evenly combined.
3. Roll the dough out into a ½-inch thick circle, dusting the top with more powdered sugar as needed to prevent sticking.

Step 3: Cut the Peppermint Patties

1. Use a small cookie cutter or the rim of a glass to cut circles that are 1 to 1 ½ inches in diameter.
2. If the dough becomes too warm and starts sticking, place it in the freezer for about 15 minutes, then continue cutting.
3. Transfer the cut patties to a parchment-lined baking sheet and freeze for another 15 minutes to firm up.

Step 4: Melt the Chocolate

1. Place 2 cups of dark melting chocolate in a microwave-safe bowl.
2. Heat in 30-second intervals, stirring well after each session to avoid burning. Repeat until the chocolate is fully melted and smooth. Let it cool slightly for 3–4 minutes before dipping.

Step 5: Coat the Peppermint Patties

1. Using a fork, dip each frozen peppermint patty into the melted chocolate, ensuring it is fully coated.
2. Allow any excess chocolate to drip off before placing the patty back onto the parchment-lined baking sheet.
3. Add sprinkles on top if desired while the chocolate is still wet.

Step 6: Chill and Enjoy

1. Place the chocolate-covered peppermint patties in the refrigerator for about 20 minutes to firm up.
2. Once set, they are ready to serve or store.