Pampered after Molly cooked eggs (7)
I believe the answer is:
coddled
This could be a double definition.
'pampered after molly' is the first definition.
'coddled' can be an answer for 'pampered' ('coddle' can be a synonym of 'pamper'). I'm unsure of the 'after molly' bit.
'cooked eggs' is the second definition.
'coddled' can be an answer for 'cooked' (coddling is a kind of cooking). I'm not sure about the 'eggs' bit.
Can you help me to learn more?
(Other definitions for coddled that I've seen before include "Cosseted" , "Pampered" .)