8 oz bittersweet chocolate, 60 to 70 percent, finely chopped
8 oz semisweet chocolate, finely chopped
1/3 cup heavy cream
3/4 teaspoon peppermint extract
8 oz good white chocolate, finely chopped
3 candy canes, crushed (or a handful of peppermint candies, crushed)
With a pencil and ruler, measure out and mark a 9 by 13-inch rectangle on a piece of parchment paper large enough to fit in a sheet pan. Flip the paper over (so the pencil marks are on the bottom), and then place the paper on a sheet pan.
Place the bittersweet chocolate in a heatproof bowl and set it over a saucepan of barely simmering water (do not allow the bottom of the bowl to touch the water). Stir occasionally until the chocolate is melted and smooth. Remove the chocolate from the heat and pour it onto the rectangle on the parchment. Using an offset spatula, spread the chocolate to fill in the rectangle. Chill until set, about 15 minutes.
While the chocolate is setting, in the same bowl you used to melt the bittersweet chocolate, combine the semisweet chocolate, cream, and peppermint extract. Warm it over the barely simmering water, stirring frequently, until the mixture is just melted and smooth. Remove the bowl from the heat and let the mixture cool until it is room temperature, about 15 minutes. Remove the sheet pan from the refrigerator and pour the semisweet chocolate mixture over the chilled chocolate rectangle. Using an offset spatula, spread the semisweet chocolate in an even layer, then chill until very cold and firm, about 1 hour.
In a clean bowl, warm the white chocolate over barely simmering water until the chocolate is smooth. Working quickly, pour the white chocolate over the firm semisweet layer, using a clean offset spatula to spread it to cover. Sprinkle with the crushed candy canes. Chill in the refrigerator just until firm, about 20 minutes.
Carefully transfer the parchment paper from the sheet pan to a large cutting board. Trim away any uneven edges of the bark so the sides are straight. Cut the bark into 2 by 9-inch (5 by 23 cm) wide strips, then cut the strips into squares or triangles.
Let the bark stand at room temperature for 10 minutes before serving. Store in an airtight container, layering sheets of wax paper or parchment paper between the layers so the pieces don’t stick to one another, in the refrigerator for up to 1 week.