Pour the milk into a small saucepan and place it over low heat.
Whisk in the cocoa powder, stirring constantly until it’s fully dissolved and the mixture is smooth, with a gentle simmer beginning (small bubbles around the edges, fragrant aroma).
Add the fresh peppermint leaves, gently pressing them with the back of a spoon to release their oils, then let the mixture simmer very low for about 5 minutes, allowing the mint to infuse the milk with a bright, refreshing aroma.
Remove the saucepan from the heat and strain out the peppermint leaves using a fine sieve, pressing gently to extract remaining flavor. Discard the leaves.
Stir in the honey or sugar, tasting and adjusting the sweetness as needed, until fully dissolved and the mixture is smooth and velvety.
Pour the hot chocolate into mugs, then top generously with whipped cream and garnish with a peppermint stick or a sprig of fresh mint for a festive look.
Serve immediately while steaming hot, enjoy the rich cocoa aroma combined with the invigorating scent of fresh peppermint.