17ounceswhite chocolate,finely chopped (don't use white chocolate chips)
6ouncescrushed peppermint candy canes,divided
Turn a large baking sheet bottom side up. Cover securely with foil. Mark a 12x9-inch rectangle on the foil. Stir the white chocolate in metal bowl set over saucepan of barely simmering water (do not allow the bottom of the bowl to touch the water) until the chocolate is melted and smooth and a candy thermometer registers 110°F (the chocolate will feel warm to the touch). Remove the pan from over the water. Pour 2/3 cup of the melted white chocolate onto the marked rectangle on the foil. Using an icing spatula, spread the chocolate to fill the rectangle. Sprinkle with 1/4 cup crushed candy canes. Chill until set, about 15 minutes.
In a medium saucepan, stir the bittersweet chocolate, cream and peppermint extract over medium-low heat until just melted and smooth. Cool to barely lukewarm, about 5 minutes. Pour the bittersweet chocolate mixture over the white chocolate rectangle. Using an icing spatula, spread the bittersweet chocolate in an even layer. Refrigerate until very cold and firm, about 25 minutes.
Re-warm the remaining white chocolate in a bowl set over barely simmering water to 110°F. Working quickly, pour the white chocolate over the firm bittersweet chocolate layer; spread to cover. Immediately sprinkle with the remaining crushed candy canes. Chill just until firm, about 20 minutes. If you let the bark go much longer than this- it will be very hard to cut neatly.
Lift the foil with the bark onto a work surface; trim the edges. Cut the bark crosswise into 2-inch wide strips. Using a metal spatula, slide the bark off the foil and onto the work surface. Cut each strip crosswise into squares. You can also cut the squares diagonally into triangles.