What food can contain a hot drink? Tempered chocolate, thickened caramel, even ice can all be used to produce a container (aka cup, mug, glass) for a liquid which, after drinking, can then also be consumed.

Is there an edible material which can be used to create a container for a hot drink? eg: Hot chocolate or coffee?

The other requirement is that this needs to be fairly straightforward to make at home; I'm aware of an espresso cup available in Italy, but this is using industrial techniques by professionals.

I have wondered about using brandy snap, but have only just learned how to make them, so have not had time to experiment.
Bread bowls are frequently used to serve thick soups, so they could probably hold coffee or hot chocolate.  Here is a patent application for an edible cup.  It might give you some ideas.  See also, this project, where an industrial designer is attempting to replace disposable containers with edible ones.  Probably critical is how hot your liquid will be, and how long you want it to be contained.