Place 5 candy canes in a bag. Smash them with a rolling pin until they are small chunks.
Line a baking sheet with parchment paper.
Melt chocolate chips in double boiler or in microwave for 3 minutes at 50% power. Heat until fully melted, stopping to stir every 30 seconds.
Pour melted chocolate onto baking sheet and spread with offset spatula to create an even layer. Place in fridge.
Melt white chocolate chips in double boiler or microwave for 3 minutes at 50% power. Heat until fully melted, stopping to stir every 30 seconds. Add 1 tablespoon oil if chocolate begins to seize.
Stir peppermint extract into melted white chocolate. Add more peppermint extract to taste, ¼ teaspoon at a time.
Pour white chocolate on top of dark chocolate. Use offset spatula to spread the chocolate and create an even layer.
Top chocolate with crushed candy canes. Place in fridge until set.
Break into pieces with your hands or a sharp knife.