Line a rimmed baking sheet with parchment paper; set aside.

Fill a pot with about 1–2 inches of water and bring to a gentle simmer. Set a heatproof bowl with the 12 ounces semisweet chocolate chips over the pot (bowl should not touch the water). Stir the chips as they heat until they are almost completely melted, then remove the bowl from the pot and stir until smooth.

Pour the melted semisweet chocolate onto the prepared parchment and use an offset spatula or knife to spread it into an even rectangle about 1/8 inch thick.

Refrigerate the sheet until the semisweet layer is cold and firm, about 20 minutes.

Place a clean heatproof bowl over the same pot of simmering water and add the 12 ounces white chocolate chips. Stir until the white chocolate is almost melted, then remove the bowl from the pot and stir until smooth.

Stir in 1/2 to 3/4 teaspoon peppermint extract to the melted white chocolate. Let the white chocolate cool for 1–2 minutes so it is warm but not hot (this helps prevent melting the set layer underneath).

Pour the white chocolate over the chilled semisweet layer and, working quickly, spread it evenly to cover.

Immediately sprinkle the 1/2 cup crushed peppermint candy canes evenly over the white chocolate and gently press so the pieces adhere.

Chill until both layers are firm, about 20–30 minutes.

Break the peppermint bark into irregular pieces or cut into squares. Store chilled in a covered container.