Produced edam variety (4)
I believe the answer is:
made
'produced' is the definition.
('make' can be a synonym of 'produce')
'edam variety' is the wordplay.
'variety' indicates anagramming the letters.
'edam' with letters rearranged gives 'MADE'.
(Other definitions for made that I've seen before include "Performed" , "Built" , "Fabricated" , "brought about" , "Created" .)