Two Soups, claiming small screen broadcast: critique extremely glowing (15)
I believe the answer is:
'glowing' is the definition.
(I know that phosphorescence is a type of fluorescence)
'two soups claiming small screen broadcast critique' is the wordplay.
'two soups' becomes 'pho pho' (pho is a type of Vietnamese soup).
'claiming' indicates putting letters inside.
'small' becomes 's' (abbreviation - e.g. clothes size).
'broadcast' indicates an anagram (letters scattered or cast around).
'critique' becomes 'ce' (I can't explain this - if you can you should believe this answer much more).
'phopho' going around 's' is 'phospho'.
'screen' with letters rearranged gives 'rescen'.
'extremely' acts as a link.
This may not be correct. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for phosphorescence that I've seen before include "Cold emitted light" , "Eerie emitted light" , "Natural glow" , "Light emitted without burning or heat" .)