Line a large baking sheet with parchment paper.
Crush the candy canes by placing them inside a heavy-duty plastic bag and striking them with a rolling pin until coarse bits remain.
Fill a pot with a small amount of water and bring to a simmer.
Place a heat-proof bowl over the pot and melt the white chocolate, stirring occasionally until smooth.
Stir the coconut oil into the melted chocolate for a glossy finish.
Remove from heat and stir in the peppermint extract until fully combined.
Pour the mixture onto the prepared baking sheet and spread it into an even layer.
Sprinkle the crushed candy canes over the surface while the chocolate is still wet.
Press the peppermint pieces gently into the chocolate to ensure they adhere.
Chill the tray in the refrigerator for at least two hours until the bark is set completely.
Break the slab into irregular shards using a sharp knife or by snapping it by hand.