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