Eunice oddly greeting fellow with a Mexican dish (9)
I believe the answer is:
enchilada
'mexican dish' is the definition.
(I've seen this before)
'eunice oddly greeting fellow with a' is the wordplay.
'oddly' indicates alternate letters.
'greeting' becomes 'hi' (hi is a kind of greeting).
'fellow' becomes 'lad' ('lad' can be a synonym of 'fellow'**).
'with' says to put letters next to each other.
The alternate letters of 'eunice' are 'enc'.
'enc'+'hi'+'lad'+'a'='ENCHILADA'
(Other definitions for enchilada that I've seen before include "Tortilla and sauce, meat" , "spicy snack" , "Tortilla with meat and chilli" , "The whole ___ -- everything (US)" , "Rolled stuffed tortilla with chilli sauce" .)