Mix the condensed milk and peppermint extract in your stand mixer using the paddle attachment, on low. Start adding the powdered sugar and beating until a stiff, dry dough forms. It shouldn't be sticky. I ended up using about half of my powdered sugar, but it can depend on humidity and other factors.
Dust a silicone baking mat or work surface with powdered sugar, like you would with flower before kneading dough. Turn out your sugar dough and form it into a ball.
Flatten the dough ball and dust it with more sugar. Use your rolling pin to roll it out to about ¼" thick, or however thick you want your peppermint patties.
Use your cookie cutter to cut out discs of dough, and arrange them on a parchment-lined baking sheet. When you've cut all you can, re-form, flatten, and cut the remainder until you've used all you can.
Freeze these disks to make them easier to work with. Chill for at least 30 minutes.
Over a double boiler, melt your chocolate and mix in the coconut oil. Keep this over low heat to keep the chocolate melted.
Taking one disc out of the freezer at a time, carefully dip them in the chocolate to coat, and arrange them on another baking sheet or a cooling rack to cool and harden. Feel free to top with sprinkles or other decorations at this point as well. Once they've all be dipped, you can put them back in the freezer to fully set.
Keep the candies refrigerated to prevent melting, and enjoy when cold!