Add the crushed candy canes, chocolate, and milk to a medium saucepan.
Cook over a medium flame, whisking occasionally as the candy canes and chocolate melt.
As the candy and chocolate melt, whisk more vigorously to incorporate ingredients.
Do not let the milk boil as that will cause it to form a skin.
Divide the hot chocolate between 4 cups; and if you wish to, top the cocoa with whipped cream and crushed candy canes. Then add a candy cane stirring stick.