Line an 11 x 17 inch cookie sheet with parchment paper. In the top of a double boiler, melt white chocolate, stirring often.
Place candy canes into a plastic bag and crushed with the flat side of a meat tenderizer. Stir pieces of candy cane and peppermint extract into the melted chocolate. Remove from heat and pour mixture onto prepared baking sheet, spreading evenly. Refrigerate until firm, about 25 to 30 minutes, and break into pieces and serve. Best if stored in an airtight container in the refrigerator, but it is totally fine left in cookie tins, etc. for gifts.