Using a sharp knife, break up the chocolate into smaller pieces. In a saucepan, combine the chopped chocolate, milk, sugar, and salt over medium-low flame. Heat and stir until the chocolate is completely melted and milk is very hot, but not boiling, about 10 minutes.
Remove from the heat and froth the chocolate milk with a mini whisk or molinillo. Divide the hot chocolate among big mugs, top each with a few marshmallows, and serve with the cinnamon sticks as stirrers.