The most common and most likely answer to this crossword clue is the 5 letter word BROIL
I've seen this crossword clue in Financial Times
B
R
O
I
L
Buddy explains!
The straight part
We know that "American cook" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case american cook = broil.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does BROIL mean?
BROIL noun- Food prepared by broiling.
- To cook by direct, radiant heat.
- To expose to great heat.
- To be exposed to great heat.
- A brawl; a rowdy disturbance.
- To cause a rowdy disturbance; embroil.
- To brawl.