His cooking includes American rice-based dish (5)
I believe the answer is:
sushi
'dish' is the definition.
(sushi is a kind of dish)
'his cooking includes american' is the wordplay.
'cooking' indicates an anagram (letters cooked up into a new form).
'includes' means one lot of letters goes inside another.
'american' becomes 'US' (United States).
'his' anagrammed gives 'shi'.
'shi' enclosing 'us' is 'SUSHI'.
'rice-based' is the link.
I am not very happy about this link. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for sushi that I've seen before include "Japanese cuisine" , "Japanese cold rice dish" , "put away in Japan" , "rice dishes" , "Cold rice dish, often with raw fish" .)