Grilled cheese may be (6)
I believe the answer is:
grated
'grilled cheese' is the definition.
'grated' can be an answer for 'cheese' (grated cheese is a kind of cheese). I am not certain of the 'grilled' bit.
'be' is the wordplay.
I cannot quite understand how this works, but
'be' could be 'rate' (rating is a kind of being) and 'rate' is located in the answer.
This explanation may well be incorrect...
'may' acts as a link.
Can you help me to learn more?
(Other definitions for grated that I've seen before include "Made a rasping sound" , "Rubbed harshly as on nerves" , "Rasped or scraped" , "was jarring" , "Made a harsh sound" .)