Line a rimmed baking sheet with parchment paper.
Melt dark chocolate chips and 1 tablespoon coconut oil together, stir in 1/2 teaspoon peppermint extract, and pour onto prepared sheet, spreading into an even layer.
Refrigerate for 15 minutes until the dark chocolate layer is set.
Melt white chocolate chips and remaining coconut oil, stir in remaining peppermint extract, and pour gently over the dark chocolate layer, spreading evenly.
Immediately sprinkle crushed candy canes over the white chocolate.
Refrigerate for 30 minutes until fully set, then break into irregular pieces.