In a medium saucepan over low heat, melt semi-sweet melting chocolates by stirring constantly until all melted. Remove from heat and stir in ¼ teaspoon peppermint extract. Pour onto prepared jelly roll pan and refrigerate.
Do the same with the white melting chocolates, by adding to a medium saucepan over low heat, stirring constantly until melted. Remove from heat and pour in the remaining peppermint extract.
Remove the pan from the refrigerator and pour white chocolate over the semi-sweet chocolate.
Sprinkle on crushed candy canes and gently press in. Refrigerate until completely hardened (about 1 hour).
When ready to serve, remove from the pan and break into small pieces.