Line the bottom and sides of a 8-inch or 9-inch square baking pan with parchment paper or aluminum foil, smoothing out any wrinkles. Or use a lined baking sheet. Set aside.

Bottom layer: Place 6 ounces of white chocolate in a small heatproof bowl or a liquid measuring cup. Add ½ teaspoon of oil. Melt in 20-second increments, stirring vigorously with a silicone spatula or spoon after each increment, until completely melted and smooth. Once melted, stir in ¼ teaspoon peppermint extract. Pour melted white chocolate into the prepared baking pan, and spread into a thin smooth layer. Place the baking pan in the refrigerator for 10–15 minutes or until almost completely set.

Middle layer: Place semi-sweet chocolate in a small heatproof bowl or a liquid measuring cup. Add ½ teaspoon of oil. Repeat melting, just as you did with the white chocolate. Once melted, stir in remaining ¼ teaspoon peppermint extract. Pour all of the semi-sweet chocolate over the white chocolate layer and spread it into a smooth layer. Place the baking pan back in the refrigerator for 10–15 minutes or until almost completely set.

Top layer: Place the remaining white chocolate in a small heatproof bowl or a liquid measuring cup. Add last ½ teaspoon of oil. Repeat melting, just as you did with the other layers. Pour over the bark layers and spread into a smooth layer. Sprinkle evenly with crushed candy canes.

Refrigerate the bark until completely set, about 1 hour. Once hardened, remove from the pan and peel off the foil or parchment. Break or cut into pieces as large or as small as you want.