Heat up milk in a sauce pot over medium-low heat. Don’t let it simmer!
Whisk in Nutella until it’s all smooth and incorporated. Let it heat through but not simmer and don't let it boil!
Once hot, take off heat and stir in Kahlua and Frangelico. If using, stir in vanilla extract as well.
Divide hot chocolate among mugs and top off with marshmallows.
If you want to do a Nutella drizzle on top of hot chocolate: add some Nutella into a piping bag and cut off the tip, leaving a small hole. Drizzle some Nutella over the marshmallows.
Notes
Need to make it non-alcoholic? You can easily make a non-alcoholic batch of Nutella hot chocolate for the kids or for yourself. All you need is milk, Nutella and a splash of vanilla extract. Follow the recipe to make the hot chocolate and just omit the alcohol.