Line a baking sheet with parchment paper. Fill the bottom of a large pot with 3” water and bring to simmer over medium heat. Reduce heat to low, then place a large heatproof bowl on top. Add semi-sweet chocolate and stir occasionally until chocolate has melted. Stir in extract. Pour into prepared baking sheet and spread into an even layer with an offset spatula. Refrigerate until set, about 20 minutes.
Over the same pot of barely simmering water, place another large heatproof bowl. Add white chocolate and stir until melted. Pour over set semi-sweet chocolate then top immediately with candy canes. Refrigerate until set, about 20 minutes.