The most common and most likely answer to this crossword clue is the 6 plus 3 letter word NUMERO UNO
I've seen this crossword clue in Financial Times
N
U
M
E
R
O
U
N
O
More clues leading to the result NUMERO UNO
- Rome’s top nun men round on never-endingly
- Leader, one of the Romans
- A wee Italian, possibly oneself
- The big cheese à l’italienne
- Uncompromising leader breaking ground no more, UN chief
- Ace Italian boss?
- One big cheese?
- The most important thing on our menu possibly
- Romeo cavorting with nun around wing of Uffizi? Berlusconi once
- Big cheese sandwich mainly found in new menu and old
Buddy explains!

The straight part
We know that "The big cheese à l’italienne" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the big cheese à l’italienne = numero uno.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.