This diner classic consists of sliced roast beef on a more or less firm bun, with a side dish of broth in which to dip it. “Au jus” means “with broth” so adding “with” to “au jus” is redundant. In fancier restaurants, items are listed entirely in French with the English translation underneath:
Tête de cochon avec ses tripes farcies
Pig’s head stuffed with tripe
Mixing the languages is hazardous if you don’t know what the original means. “With au jus broth” is also seen from time to time. People generally know what a French dip sandwich is, and they’ll see the broth when it comes. Why not just call it a “French dip?”
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