In a small saucepan, melt the semi-sweet chocolate on low heat until melted and smooth. Be sure to stir constantly and watch closely to not burn! This should only take 3-4 minutes. Stir in 1 teaspoon peppermint extract.
Line a 9x13 pan with parchment paper. Pour in the melted semi-sweet chocolate and spread evenly. Put in the freezer and freeze for 15 minutes or until solid.
While semi-sweet chocolate layer is freezing, melt the white chocolate the same way you did the semi-sweet on a stove, stirring constantly and melting until smooth. Stir in the other teaspoon peppermint extract.
With a food processor or kitchen mallet, smash the candy canes into small pieces. We like still some larger chunks, so don't go too crazy here.
Remove semi-sweet chocolate layer from the freezer. Spread the melted white chocolate layer on top, smoothing until even and flat. Sprinkle the candy cane pieces into the melted white chocolate. Freeze for another 15 minutes.
Once solid, remove from freezer and break into pieces. Store in a sealed reusable bag or container on the counter for up to 2 weeks or in the freezer for up to 6 months.