Lady promoting European dairy product (4)

I believe the answer is:

edam

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'dairy product' is the definition.
(Edam is an example)

'lady promoting european' is the wordplay.
'lady' becomes 'Eda'.
'promoting european' becomes 'm' (I am not sure about this - if you are sure you should believe this answer much more).
'eda'+'m'='EDAM'

Can you help me to learn more?

(Other definitions for edam that I've seen before include "Kind of cheese" , "Dutch 8 across" , "Made into a nice cheese" , "Danish cheese" , "Round, yellow cheese" .)

I've seen this clue in The Independent.

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