Line an 8x8 pan with parchment paper. I like to cut two pieces and have one going in each direction so that the whole pan is covered.
Melt the dark chocolate in a microwave-safe bowl in 30-second intervals, stirring after each interval, until completely melted and smooth. It will likely take 1 to 3 minutes (depending on your microwave). Do not overheat as the chocolate will scorch. Stir 1/2 teaspoon of the peppermint extract. Pour melted chocolate into the prepared pan and spread it with the back of a spoon until an even layer is formed. Place in the fridge to set for about 30 minutes or until firm to the touch.
While dark chocolate is chilling, crush your candy canes. You can do this in a food processor or place candy canes in a freezer bag and crush using a rolling pin or the bottom of a glass. Once candy canes are crushed, set aside.
Once dark chocolate has set start, melt the white chocolate in a microwave-safe bowl in 30-second intervals, stirring after each interval, until completely melted and smooth. It will likely take 1 to 3 minutes (depending on your microwave). Stir in remaining 1/2 teaspoon of peppermint extract. Pour melted white chocolate over the dark chocolate and spread it with the back of a spoon until an even layer is formed.
Sprinkle the candy cane pieces evenly over the white chocolate layer and lightly press with your hands.
Place pan back in the fridge to chill until set, about 30-60 minutes.
Once chocolate has hardened, bring it out of the fridge and let it sit at room temp for 5-10 minutes before cutting or breaking into pieces. If you try to cut it when it's too cold the chocolate layers may separate.
Store peppermint bark in a dark, cool place. It should last about 7-10 days in a cool kitchen or even longer (about 3 weeks or so) in the fridge or freezer. If you keep the bark in the fridge or freezer, be sure to bring it out and let it rest for 5-10 minutes before eating because the chocolate gets really hard when chilled.