Line a 9x13-inch baking pan with parchment paper or wax paper.
Sprinkle ⅓ of the crushed peppermint candy or crushed candy canes evenly over the bottom of the lined pan.
Melt the milk chocolate or dark chocolate in the top of a double boiler over barely simmering water, stirring often and scraping down the sides with a rubber spatula until smooth. You can also melt the chocolate in short intervals in the microwave, stirring between each one.
Pour the melted milk chocolate or dark chocolate over the crushed peppermint in the prepared pan. Spread it into an even layer.
Sprinkle another ⅓ of the crushed peppermint over the chocolate layer.
Refrigerate until the chocolate is firm, about 25 minutes.
Melt the white chocolate in the top of a double boiler over barely simmering water, stirring often and scraping down the sides with a rubber spatula until smooth. Stir in the peppermint extract.
Let the white chocolate cool for 10 to 20 minutes, or until it is about 120°F. It should still be melted and pourable, but not so hot that it melts the chocolate layer underneath.
Remove the pan from the refrigerator. Pour the cooled white chocolate over the firm chocolate layer and spread it gently into an even layer.
Sprinkle the remaining ⅓ of the crushed peppermint over the white chocolate layer.
Refrigerate until the white chocolate is firm, about 30 minutes.
Remove the pan from the refrigerator and let the peppermint bark sit at room temperature for about 5 minutes before cutting or breaking it into pieces. This helps keep it from shattering too much.
Cut or break into pieces and serve.