Line a 9-inch square baking pan flat with parchment paper and set aside.
Add chopped dark chocolate to a microwave-safe bowl and microwave in 30 second increments on half-power, stirring well after each increment, until just melted and smooth.
Separately melt ¾ teaspoon of the coconut oil in the microwave, then stir ½ teaspoon of the peppermint extract into the oil.
Stir into the melted dark chocolate until evenly combined.
Pour the melted chocolate into the parchment-lined pan and spread into an even layer with a spatula.
Chill for 10-15 minutes or until just set.
Chop the white chocolate, add it to a microwave-safe bowl, then melt it in the same way as the dark chocolate.
Separately melt the remaining ¾ teaspoon of coconut oil, stir in the remaining ½ teaspoon of peppermint extract, and stir into the white chocolate.
Once the dark chocolate layer has just set, pour over the white chocolate and gently spread it around to cover in an even layer.
Scatter chopped Oreo cookie pieces and crushed candy canes over the white chocolate and lightly press so they adhere to the bark.
Return the pan back to the fridge to harden fully before slicing, around 2-3 hours.
Store Oreo peppermint bark in an air-tight container for several weeks in the fridge, or for shorter bursts at room temperature.
