I'm not sure one will find authoritative references for this yet. Google ngram results (see below) are totally misleading, all false positives (typos, exercises in novel spelling, proper nouns) as far as I've checked. And only 8 000 Google hits for "the uze", many containing non-standard grammar, but:
uze
Short for "usual." Indicates a "ho-hum" attitude and a tonal sense of comfort with the person with whom you are speaking.
- "What's going on in your life?"
- "You know, the uze."
Urban Dictionary; Andy{!}; 2004
I suppose the caveats apply in many restaurants, though one would expect more of a 'might I recommend chef's special, sir' attitude at the Ritz.