Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the sides.
Melt the semisweet chocolate in a microwave-safe bowl in 30-second bursts, stirring after each, until smooth (or melt it over a pot of barely simmering water).
Spread the dark chocolate evenly in the lined pan with an offset spatula. Refrigerate 15 to 20 minutes, until set but not rock hard.
Melt the white chocolate gently in 20-second bursts, stirring well each time, until just smooth. Stir in the peppermint extract.
Pour the white chocolate over the dark layer and spread it evenly to the edges.
Sprinkle the crushed candy canes over the top right away and press them in lightly.
Refrigerate 30 minutes to 1 hour, until firm. Lift the bark out by the parchment and break or cut it into about 24 pieces.