Caught method, and mine turned into a dish (4,4)
I believe the answer is:
chow mein
'a dish' is the definition.
(chow mein is a kind of dish)
'caught method and mine turned' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'method' becomes 'how' (I've seen this in another clue).
'and' means one lot of letters go next to another.
'turned' indicates an anagram.
'mine' anagrammed gives 'mein'.
'c'+'how'+'mein'='CHOW-MEIN'
'into' acts as a link.
(Other definitions for chow mein that I've seen before include "Chinese-American dish" , "Chinese dish of noodles, meat and veg" , "Chinese-style dish of shredded meat(s) and fried noodles" , "Chinese/US noodle dish" , "take-away food" .)