Crossword Genius

Cook right through in plenty of water (6)

Ross

I believe the answer is:

stream

I'm a little stuck... Click here to teach me more about this clue!

'water' is the definition.
(stream is a kind of water)

'cook right through in plenty' is the wordplay.
I cannot really understand how this works, but
'right' could be 'r' (common abbreviation) and 'r' is present in the answer.
'cook' could be 'steam' (steaming is a kind of cooking) and 'steam' is present in the leftover letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

'of' is the link.

Can you help me to learn more?

(Other definitions for stream that I've seen before include "Small narrow river" , "pupils pour out" , "Constant flow of liquid" , "Brook or rivulet" , "flower" .)

I've seen this clue in the Evening Standard.
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