Line a baking sheet with parchment paper; set aside.
Unwrap the candy canes and place in a small Ziploc bag. Using a rolling pin, smash them into small pieces.
Place the dark chocolate in a medium, heatproof bowl. Microwave in 15-second increments, stirring after each, until completely melted. Stir the peppermint extract into the melted chocolate. Using an offset spatula, spread the melted chocolate in an even, thin layer on the prepared cookie sheet in an approximately 8-inch rectangle The chocolate will not cover the entire surface of the sheet pan. Place the cookie sheet in the refrigerator while you prepare the white chocolate.
Melt the white chocolate using the same microwave method. Remove the cookie sheet from the refrigerator and, using an offset spatula, spread the melted white chocolate on top of the dark chocolate layer.
Immediately sprinkle the crushed candy canes on top of the melted white chocolate and gently press into the chocolate to adhere.
Refrigerate at least 30 minutes. Use a sharp knife to break the bark into pieces. Store the bark in an airtight container in the refrigerator.