Line a 9x13-inch baking sheet with parchment paper and set aside.
Microwave dark chocolate in a microwave-safe bowl at 30-second intervals, stirring between each, until completely smooth.
Spread chocolate evenly on prepared sheet with a spatula; refrigerate 15-20 minutes until firm.
Melt white chocolate by same method; stir in peppermint extract.
Spread white chocolate evenly over dark layer.
Immediately sprinkle candy canes over top; press gently to adhere.
Refrigerate 30 minutes until completely set; break into irregular pieces and store airtight.