Line an 11x17-inch baking sheet with parchment paper.
Melt white chocolate chips in a microwave-safe glass bowl on 50% power for 3 minutes. Stir well until bowl is no longer warm. Heat for 3 minutes more; stir. Heat for 1 minute more and stir; repeat as necessary until chocolate is completely smooth.
Stir candy canes and peppermint oil into the melted chocolate until well combined. Spread onto the prepared baking sheet. Smooth with a spatula. Refrigerate until set, 30 minutes to overnight. Break into pieces and store in an airtight container.