In a small pot, combine the whole milk, cocoa powder, and granulated sugar. Heat on medium-low, stirring constantly to dissolve the sugar and cocoa until smooth.

Add the chocolate chips to the pot. Continue stirring until the chocolate chips melt completely. Avoid boiling.

Pour the hot chocolate into a mug. Stir in the peppermint schnapps until well combined. Top with whipped cream and crushed candy canes. Serve immediately.