Add the peppermint candy into a zipper baggie , seal well, and use a rolling pin to crush into fine particles. Set aside.
Melt the white chocolate or vanilla candy coating in a microwave-safe bowl for 30 seconds, then in 15-second increments, stirring gently but often, until it's thoroughly melted. Don't overheat, or it will burn and seize.
Using a fork: Dip the Oreo cookies into the melted candy coating/white chocolate and let the excess drip off.
Place the well-coated OREOs onto the parchment-covered work surface and sprinkle the center of each coated OREO with the crushed candy.
Allow about 1 hour for the coating to set before serving. You can move them to the fridge or freezer or a faster set, about 20 minutes.