Prepare the pan. Line the bottom and sides of an 8-inch or 9-inch square baking pan with parchment paper or aluminum foil. Press the liner into the corners so the layers will lift out easily. Set the pan aside.

Make the bottom white chocolate layer. Melt 6 ounces of white chocolate with 1/2 teaspoon of vegetable oil or coconut oil in the microwave in 20-second increments, stirring between increments until smooth. Stir in 1/4 teaspoon peppermint extract. Pour the melted white chocolate into the prepared pan and spread it evenly with an offset spatula or the back of a spoon. Refrigerate for 10 to 15 minutes until almost set.

Make the middle chocolate layer. Melt the semi-sweet or bittersweet chocolate with the remaining 1/2 teaspoon of oil in the microwave, again using 20-second bursts and stirring until smooth. Stir in the remaining 1/4 teaspoon peppermint extract. Pour this melted chocolate over the white chocolate layer and spread it evenly. Return the pan to the refrigerator for another 10 to 15 minutes.

Add the top white chocolate layer and topping. Melt the remaining 6 ounces of white chocolate with the last 1/2 teaspoon of oil, stirring until smooth. Pour this white chocolate over the previous layers and spread evenly. Immediately sprinkle the crushed candy canes over the top and gently press them into the chocolate so they adhere.

Chill and finish. Refrigerate the assembled bark until completely set, about 1 hour. Once firm, lift the bark from the pan using the parchment or foil, then cut or break it into pieces. Store in an airtight container in the refrigerator for up to 3 weeks.