Make the chocolate base: In a small saucepan, whisk cocoa powder, sugar, and a splash of milk over low heat until smooth, glossy, and lump-free, 30–60 seconds.
Heat and froth the milk: Add the remaining milk and a pinch of salt. Warm gently until steaming, not boiling.
Froth with a whisk, milk frother, or blender for 10–20 seconds.
Brew the coffee: Pull your espresso shot or brew strong coffee. Aim for bold flavor to stand up to the chocolate.
Flavor it: Remove the milk from heat. Stir in peppermint and vanilla extracts.
Start with 1/8 to 1/4 teaspoon peppermint, then taste; add more only if needed.
Assemble: Pour the coffee into a mug. Add the chocolate-mint milk and stir well to combine.
Finish: Top with whipped cream. Garnish with crushed candy cane or chocolate shavings for a festive touch.
Serve hot.