Charlie cuts additives put in food hampers (9)

'hampers' is the definition.
Although both the answer and definition are verbs in their -s form, I can't understand how one could define the other.

'charlie cuts additives put in food' is the wordplay.
I cannot quite understand how this works, but
'charlie' could be 'c' (phonetic alphabet) and 'c' is found within the answer.
'food' could be 'e' (E is an example) and 'e' is found within the answer.
The remaining letters 'numbers' 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?