In a small sauce pot over medium low heat add the chocolate, milk, cream and powdered sugar.
Stir until the mixture becomes thick and silky. Add in the vanilla extract and stir until incorporated.
If the mixture is too thick add a bit more milk to thin it out. If the mixture is too thin then continue to heat it until it thickens.
Be sure the keep this over medium-low heat so you do not burn the chocolate.
Serve warm. You can serve with whipped cream or marshmallows, but that would not be the "correct" way to serve European Hot Chocolate. But, drink it however you want!!!
Notes:
* Use the best chocolate you can find or afford (Lindt, Godiva, Ghiradelli...) If you can only find bars of chocolate just break them up before placing them in the pot for easier melting.
* If you want to add Grand Marnier, peppermint extract, espresso... to the drink then add to the mixture when you add the vanilla.