Line an 8-inch square pan with parchment paper, covering the edges for easy lifting.

In a microwave-safe bowl, melt 2 chopped white chocolate bars with 1/2 tsp vegetable oil until smooth, about 1-2 minutes.

Stir in 1/2 tsp peppermint extract and spread evenly in the prepared pan. Refrigerate for 10 minutes.

Melt the bittersweet chocolate with 1/2 tsp vegetable oil in another bowl, stirring until silky.

Add 1/4 tsp peppermint extract, mix thoroughly, then spread over the chilled white chocolate. Refrigerate for another 10 minutes.

Melt the remaining chopped white chocolate with 1/2 tsp vegetable oil until smooth.

Combine with the remaining 1/4 tsp peppermint extract, then spread over the layer of bittersweet chocolate. Top with crushed candy canes.

Refrigerate the entire pan for about an hour to let the layers firm up. Once set, break into squares and serve.