Greek character initially eating baked food (3)
I believe the answer is:
pie
'baked food' is the definition.
(I've seen this before)
'greek character initially eating' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'initially' suggests taking the first letters.
The first letter of 'eating' is 'e'.
'pi'+'e'='PIE'
(Other definitions for pie that I've seen before include "something with custard, say" , "Pecan or blueberry dish?" , "See 6" , "welcome luxury" , "Bird - dish - mixed type" .)