Chop the dark chocolate or measure out chocolate chips, placing them in a bowl ready to melt.
Pour the whole milk into a saucepan and set over medium heat. Warm gently, stirring occasionally, until you see tiny bubbles forming around the edges—this is about 70°C (160°F). Keep an eye on it to prevent boiling.
Add the chopped chocolate or chocolate chips into the warm milk. Stir continuously with a whisk until the chocolate melts completely and the mixture becomes glossy and smooth, filling your kitchen with a rich cocoa aroma.
Stir in the peppermint syrup or extract, blending well. Taste the mixture; if you'd like a stronger mint flavor, add a bit more, stirring until evenly incorporated.
Add the sugar and vanilla extract, stirring until fully dissolved. This balances the richness and adds warmth to the flavor profile. Remove the saucepan from heat once everything is well combined.
Pour the hot chocolate into your pre-warmed mugs, filling them generously. Top with whipped cream and sprinkle with crushed peppermint candies for a festive look and extra crunch.
Serve immediately, savoring the creamy, glossy surface and the refreshing aroma of peppermint with each sip. Enjoy the cozy warmth and festive flavors!