Place the entire package of Oreo cookies into a food processor. Pulse until the cookies are turned into fine crumbs. You should not have any large chunks remaining, as a fine texture makes for a smoother truffle center.
In a large mixing bowl, combine the Oreo crumbs, the softened cream cheese, and the peppermint extract. Use a hand mixer or a sturdy spatula to blend until the mixture is uniform and no white streaks of cream cheese remain.
Line a baking sheet with parchment paper. Scoop about one tablespoon of the mixture at a time and roll it between your palms to form a smooth ball, about 1 inch in diameter. Place each ball on the prepared baking sheet.
Place the baking sheet in the refrigerator for at least 1 hour, or in the freezer for 30 minutes. Chilling the balls is essential; it prevents them from falling apart or melting when you dip them into the warm chocolate later.
Place the white chocolate melting wafers in a microwave-safe bowl. Microwave in 30-second intervals, stirring in between each session, until the chocolate is completely smooth and melted. Be careful not to overheat it, or the chocolate may seize.
Using a fork or a dipping tool, submerge each chilled Oreo ball into the melted white chocolate. Tap the fork against the side of the bowl to let the excess chocolate drip off. Place the ball back on the parchment paper and immediately sprinkle with crushed candy canes before the chocolate sets.