That man's after reduced fast food in deli? (6)
I believe the answer is:
quiche
'food in deli?' is the definition.
'quiche' can be an answer for 'food' (quiche is a kind of food). I'm not certain of the 'in deli?' bit.
'that man's after reduced fast' is the wordplay.
'that man' becomes 'Che'.
'after' is a charade indicator (letters next to each other).
'reduced fast' becomes 'qui' (I can't justify this - if you can you should believe this answer much more).
'che' after 'qui' is 'QUICHE'.
Can you help me to learn more?
(Other definitions for quiche that I've seen before include "Open tart with egg filling" , "Cheese and bacon pastry dish" , "Baked egg flan" , "French dish?" , "Savoury tart with egg-based filling" .)