In a mixing bowl, combine the powdered sugar, sweetened condensed milk, peppermint extract, and vanilla extract. Use an electric mixer or whisk until smooth and well-blended.
Roll the mixture into small balls or flatten it into disk shapes approximately ½ inch thick, and place them on a baking sheet lined with parchment paper.
Refrigerate the baking sheet for about 60 minutes to allow the patties to firm up.
Melt the dark chocolate chips and coconut oil together in a microwave-safe bowl, heating in 30-second increments until fully melted and smooth, stirring in between.
Remove the patties from the refrigerator. Using a fork, dip each patty into the melted chocolate, ensuring it is completely coated. Tap the fork on the edge of the bowl to remove excess chocolate.
Place the chocolate-covered patties back onto the parchment-lined baking sheet. Allow the chocolate to set completely at room temperature or refrigerate for quicker setting.
Once the chocolate is hardened, enjoy your homemade peppermint patties!