Order sponge that's cut or a piece of cake inside cafe (6,5)
I believe the answer is:
greasy spoon
'cafe' is the definition.
(I've seen this before)
'order sponge that's cut or a piece of cake inside' is the wordplay.
'order' indicates anagramming the letters.
'that's cut' means to remove the last letter.
'a piece of cake' becomes 'easy' (I've seen this before).
'inside' means one lot of letters goes inside another.
'sponge' with its final letter taken away is 'spong'.
'spong'+'or'='spongor'
'spongor' anagrammed gives 'grspoon'.
'grspoon' going around 'easy' is 'GREASY SPOON'.
(Other definitions for greasy spoon that I've seen before include "diner, by the way" , "Cafe (sl.)" , "Roadside cafe" , "Naff caff" , "Workers' cafe" .)