Favours central character in pan-Slav broadcast? (7)

I believe the answer is:

largess

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'pan-slav broadcast?' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.

'favours central character' is the wordplay.
'favours central' becomes 'larg' (I am not sure about this - if you are sure you should believe this answer much more).
'character' becomes 'ess' (the letter S).
'larg'+'ess'='LARGESS'

'in' is the link.

Can you help me to learn more?

(Other definitions for largess that I've seen before include "Generosity" , "Bounty" .)

I've seen this clue in The Times.

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