In a medium mixing bowl, whisk together powdered sugar and cocoa powder until well combined.
Add the sweetened condensed milk and peppermint extract to the dry ingredients. Mix until a dough forms. If the mixture is too sticky, add a little more powdered sugar until you can handle it.
Dust your hands with powdered sugar and take small portions of the peppermint mixture. Roll them into small balls and then flatten them into patties about 1/4 inch thick. Place the patties on a parchment-lined baking sheet.
Once you have shaped all the patties, place the baking sheet in the freezer for about 30 minutes to firm them up.
While the patties are chilling, prepare the chocolate coating. In a small microwave-safe bowl, combine dark chocolate chips and coconut oil. Microwave in 30-second intervals, stirring in between until completely melted and smooth.
Dip each chilled peppermint patty into the melted chocolate, ensuring it is fully coated, then return it to the parchment-lined baking sheet.
Once all patties are coated, refrigerate for another 15-20 minutes until the chocolate hardens completely.
Serve chilled or at room temperature and enjoy your homemade peppermint patties!