In extremes of poverty, she always has breakfast! (5)

I believe the answer is:
peggy
'breakfast' is the definition.
Both the answer and definition are singular nouns.
Maybe they are linked in a way I don't understand?
'in extremes of poverty she always' is the wordplay.
'in' indicates putting letters inside.
'extremes of' says to hollow out the word (remove centre letters) (only the letters at the extremes of the word).
'she always' becomes 'egg' (I can't justify this - if you can you should believe this answer much more).
'poverty' with its middle removed is 'py'.
'py' placed around 'egg' is 'PEGGY'.
'has' acts as a link.
Can you help me to learn more?
(Other definitions for peggy that I've seen before include "one associated with Sue" , "Dolly < bird" , "- - Lee, popular singer" .)
