Place the peppermint candies or mini candy canes into a zip-top bag. Use a rolling pin or meat mallet to crush them into smaller pieces, leaving some chunks for texture. Alternatively, use a food processor for even finer crushed candy cane pieces.
Cover a baking sheet or cookie sheet with parchment paper, wax paper, or aluminum foil.
Melt the chocolate over the top of a double boiler and add 1/2 teaspoon peppermint extract. Or, in a microwave-safe bowl, melt the dark chocolate chips in 30-second intervals, stirring with a rubber spatula or wooden spoon after each interval until smooth.
Pour the melted dark chocolate onto the prepared pan. Use the back of a spoon to spread it into an even layer about ΒΌ inch thick. Allow this bottom layer to set in a cool place (refrigerator) while you prepare the next layer.
Repeat the melting process with the white chocolate chips or bars and add in the other 1/2 teaspoon peppermint extract; however, remove them from the heat just before all the chocolate has melted. Stir the chocolate and allow it to continue to melt off the heat.
Allow the white chocolate to cool slightly, and then pour the melted white chocolate over the set dark chocolate layer. This will help prevent it from smearing into the chocolate layer, creating swirls instead of layers. Spread it gently to create an even top layer.
Sprinkle the crushed peppermint candies evenly across the melted white chocolate while still soft.
Allow the bark to cool and harden completely in a cool place or refrigerator. Once the chocolate bark is fully set, transfer it to a cutting board for the cutting process.
Use a sharp knife or your hands to break the bark into smaller pieces. Store peppermint bark in an airtight container in a cool place for up to a couple of weeks.