Here is the definition according to Merriam-Webster.
adjective | \ō-ˈzhü(s), -ˈjüs; ō-zhue\
: served in the juice obtained from roasting
The origin of this term is French, literally meaning, “with juice”. So, beware of the temptation to say “with au jus”. Horror of horrors! You would be committing a grammar crime. You wouldn’t want to say, “with with juice”, now would you?
For example, this recipe is called “Prime Rib Au Jus” – not “Prime Rib with Au Jus”.
There you go! You have now had a lesson in another cooking term AND grammar. 🙂