Begin by lining a baking sheet with parchment paper, ensuring it covers the entire surface.
In a medium saucepan, melt the semi-sweet chocolate over low heat, stirring frequently until smooth. Be cautious not to overheat the chocolate.
Once melted, pour the semi-sweet chocolate onto the prepared baking sheet. Use a rubber spatula to spread it evenly into a rectangle, about 1/4 inch thick. Place it in the refrigerator to set for approximately 10 minutes.
While the semi-sweet chocolate is setting, melt the white chocolate in a heatproof bowl over a saucepan of simmering water or in the microwave (in 30-second intervals, stirring in between) until smooth.
Once melted, remove the white chocolate from heat. Stir in the peppermint extract and a pinch of salt for extra flavor.
Pour the melted white chocolate over the set semi-sweet chocolate layer. Spread it evenly, ensuring it covers the dark chocolate completely.
Before the white chocolate sets, sprinkle the crushed candy canes evenly over the top. Gently press down to ensure they stick.
Return the baking sheet to the refrigerator and let it chill for at least 30 minutes, or until completely set.
Once set, break the peppermint bark into pieces using your hands or a knife.