Whisk evaporated milk, regular milk, chocolate, sugar, salt and coffee powder in a saucepan over medium heat until the chocolate is melted.
Whisk in the vanilla. Cover and cook on low heat for 7-8 minutes more, stirring occasionally.
Remove from heat and let the hot cocoa rest (still covered) for 5 minutes, so it can thicken a bit.
Top with marshmallows and peppermint pieces. Serve immediately.