Cook with waiters at hairdressers in conversation? (8)

I believe the answer is:

barbecue

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'cook' is the definition.
(thesaurus)

I don't understand the remainder of the clue.

(Other definitions for barbecue that I've seen before include "Cuba beer for outdoor meat meal" , "Grill for outdoor cooking" , "Meal cooked outside" , "Outdoor party (full of sizzle?)" , "A picnic with grilled meats" .)

I've seen this clue in The Times.

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