Celebrate homecoming, initially drawing flak at Little Chef, sadly (4,3,6,4)

I believe the answer is:

kill the fatted calf

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'celebrate homecoming initially drawing flak at little chef sadly' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'initially drawing flak at little chef sadly' is the wordplay.
'initially' says to take the initial letters.
'sadly' indicates anagramming the letters.
The first letter of 'drawing' is 'd'.
'd'+'flak'+'at'+'little'+'chef'='dflakatlittlechef'
'dflakatlittlechef' is an anagram of 'KILL THE FATTED CALF'.

Can you help me to learn more?

(Other definitions for kill the fatted calf that I've seen before include "celebrate homecoming?" , "Dispatch podgy young Kerry" , "Celebrate extravagantly" .)

I've seen this clue in The Times.

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