Fresh portion of heavenly cheese, allegedly (3,4)

I believe the answer is:
new moon
'cheese allegedly' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'fresh portion of heavenly' is the wordplay.
I cannot quite see how this works, but
'fresh' could be 'new' (synonyms) and 'new' is found in the answer.
'of' could be 'o' and 'o' is found within the answer.
The remaining letters 'mon' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for new moon that I've seen before include "emergent body" , "Earth's satellite when appearing as a narrow crescent" , "Phase of Earth's satellite" , "Crescent shaped lunar appearance" , "First phase(s) of lunar cycle" .)
