In a large bowl, add the powdered sugar, softened vegan butter, peppermint extract and coconut milk. Using a handheld mixer or stand mixer with the paddle attachment, mix, starting on low and increasing to medium speed. At first it will look very dry and crumbly, but after a few minutes it well soften and be more of a dough. If it's too wet and sticky, add a little more powdered sugar. It should feel like play dough. Set aside.
Line a baking sheet with parchment paper. Scoop about a tablespoon at a time of the peppermint mixture and shape into a disc. Place the patties in a single layer on the prepared pan, and repeat until you have used all of the mixture.
Place the patties in the refrigerator for 45 minutes, or freeze for 15 minutes. This will help them harden a bit and set.
Melt the chocolate and coconut oil over a double boiler, preferably, or in the microwave. Stir well so it's smooth. Let it cool for just a few minutes.
Remove the patties from the refrigerator or freezer and dip one patty at a time into the chocolate mixture, using a fork to help you coat it on all sides. Return back to the parchment lined pan.
Place the pan back in the freezer for 5 minutes to harden, or the refrigerator for 15 minutes. Once set, place in a container with a lid and store in the refrigerator. At room temperature, the chocolate will start to melt. They will keep for about 2 weeks or longer in the freezer. Enjoy!