Prepare a baking sheet by lining it with parchment paper. In a plastic bag, add the peppermint candies and crush them into small pieces using a rolling pin.
In a microwave-safe bowl, combine the dark chocolate chips. Melt them in the microwave at short intervals, stirring in between, until smooth and glossy.
Spread the melted dark chocolate over the prepared baking sheet, smoothing it into an even layer about 1/4-inch thick. Let it cool at room temperature for around 5 minutes, or until just set but still slightly tacky.
While the dark chocolate sets, melt the white chocolate in a separate bowl, using the microwave method. Stir in the peppermint extract to infuse flavor. Allow the mixture to rest for a minute until it thickens slightly.
Carefully pour the white chocolate over the dark chocolate layer. Gently coax it to the edges to cover completely without mixing the two layers. Immediately sprinkle the crushed peppermint over the top and lightly press them in for adherence.
Refrigerate the entire piece until completely firm, about 25–30 minutes. Once set, break or cut into squares for serving.