Fine oil improved seasoned mayonnaise (5)

I believe the answer is:

aioli

I'm a little stuck... Click here to teach me more about this clue!

'seasoned mayonnaise' is the definition.
'aioli' can be an answer for 'mayonnaise' (mayonnaise seasoned with garlic). I am unsure of the 'seasoned' bit.

'fine oil improved' is the wordplay.
'fine' becomes 'ai' (resembles A1, informal term for top quality).
'improved' indicates an anagram.
'oil' with letters rearranged gives 'oli'.
'ai'+'oli'='AIOLI'

Can you help me to learn more?

(Other definitions for aioli that I've seen before include "11 [SAUCE]" , "Mayonnaise with garlic" , "garlic sauce" , "mayonniase" , "Garlicky mayonnaise" .)

I've seen this clue in The Times and The Sunday Times.

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