In a mixing bowl, combine the powdered sugar, cocoa powder, and softened butter. Use a spoon or spatula to blend until the mixture is crumbly.
Add the sweetened condensed milk and peppermint extract to the bowl. Mix until a smooth dough forms. If the dough is too sticky, you can add a bit more powdered sugar as needed.
Once the dough is ready, place it on a piece of parchment paper and use a rolling pin to roll it out to about ¼ inch thick.
Cut out circles using a cookie cutter or a glass, and place the circles on a baking sheet lined with parchment paper. You should have about 12 circles.
Refrigerate the mint centers for at least 15 minutes to firm up.
While the mint centers chill, prepare the chocolate by melting it in a double boiler or microwave, stirring until smooth. If using a microwave, heat in 30-second intervals, stirring between each until fully melted.
If desired, you can add vegetable oil to the melted chocolate to achieve a smoother consistency.
Once the mint patties are firm, dip each one into the melted chocolate, ensuring they are fully coated. Use a fork to lift them out, letting any excess chocolate drip off.
Place the chocolate-covered patties back on the parchment-lined baking sheet and allow them to set at room temperature or in the refrigerator to harden.
Once the chocolate has hardened, your peppermint patties are ready to enjoy!