Pour the milk into a medium saucepan and set over low heat, warming until it just begins to steam and small bubbles form around the edges, about 3-5 minutes.
Add the cocoa powder to the warm milk and whisk vigorously until completely dissolved and the mixture is smooth, about 1-2 minutes. You should see a rich, velvety texture forming as the cocoa melds into the milk.
Crumble the fresh peppermint leaves and gently crush them with your fingers to release their aroma. Add these to the milk mixture, stirring gently to infuse the flavor.
Stir in the honey or sugar, tasting as you go. Keep whisking until the sweetener has dissolved completely, about 1 minute, and the mixture is fragrant.
If using, add a few chocolate chips or melting wafers to the saucepan and stir continually over low heat until melted and fully incorporated, about 2-3 minutes. This adds extra richness and a glossy finish.
Remove the saucepan from heat, and strain the mixture through a fine-mesh sieve into two mugs to catch the peppermint leaves and any chocolate bits, ensuring a silky smooth drink.
Garnish with whipped cream, a peppermint stick, or a light dusting of cocoa powder for festive flair. Serve immediately while warm and fragrant.