Line a large baking sheet with parchment paper or a silicone baking mat. Set aside.
Add the chopped semi-sweet chocolate and ½ teaspoon of oil to a microwave-safe bowl and microwave in 20-30 second increments, stirring well after each increment, until completely melted and smooth. Stir in ¼ teaspoon peppermint extract.
Pour the melted chocolate onto the parchment paper or silicone baking mat and spread it around into one even layer (I like to make an 8x10 rectangle).
Transfer the baking sheet with the semi-sweet chocolate to the refrigerator to chill for 20 minutes, or until just set.
When the semi-sweet chocolate is almost chilled, place the chopped white chocolate and remaining ½ teaspoon of oil in a microwave-safe bowl. Microwave in 20-30 second increments, stirring well after each increment, until completely melted and smooth. Stir in the remaining ¼ teaspoon peppermint extract. Set aside to cool slightly.
Once the semi-sweet chocolate layer is just set and firm to the touch, remove it from the refrigerator. Pour the slightly cooled white chocolate on top of the semi-sweet chocolate and spread it around into one even layer.
Sprinkle the crushed candy canes on top, then transfer to the refrigerator for 45 minutes or until the white chocolate layer is fully chilled and set.
Break or slice into pieces, serve, and enjoy!