Line a 9×13-inch baking sheet with parchment paper or a silicone baking mat. Ensure the parchment hangs slightly over the edges so you can easily lift the bark out later. Place your candy canes in a heavy-duty plastic bag and crush them into small bits using a rolling pin or a heavy spoon.

Place the dark chocolate chips in a microwave-safe bowl. If using coconut oil, add half a teaspoon now. Microwave in 30-second intervals, stirring well between each session, until the chocolate is completely smooth. Stir in 1/4 teaspoon of peppermint extract. Pour the chocolate onto the prepared baking sheet and spread it into an even layer using an offset spatula.

Place the baking sheet in the refrigerator for about 10 to 15 minutes. You want the chocolate to be set but not rock hard. If the bottom layer is too cold, the top layer might slide off later. While it chills, prepare your white chocolate.

Repeat the melting process with the white chocolate chips and the remaining coconut oil. White chocolate burns more easily than dark chocolate, so use 20-second intervals and stir frequently. Once smooth, stir in the remaining 1/4 teaspoon of peppermint extract.

Remove the tray from the fridge. Pour the melted white chocolate over the dark chocolate layer. Use a clean spatula to spread it gently to the edges. Work quickly so the warmth of the white chocolate does not melt the bottom layer too much. Immediately sprinkle the crushed candy canes over the wet white chocolate, pressing them down very lightly so they stick.

Return the tray to the refrigerator for at least 1 hour, or until the bark is completely firm. Once set, lift the parchment paper out of the pan. Use your hands to snap the bark into irregular, rustic pieces, or use a sharp knife for more uniform squares. Serve immediately or package for gifting.