Egg with no alcohol in mixed-up state (8)

I believe the answer is:
omelette
'egg' is the definition.
The answer and definition can be both things that one consumes for nourishment as well as being singular nouns.
Perhaps you can see a link between them that I can't see?
'no alcohol in mixed-up state' is the wordplay.
I cannot really see how this works, but
'no' could be 'o' (resembles 0 - 'no' can mean 'zero') and 'o' is found in the answer.
'state' could be 'me' and 'me' is present in the answer.
The remaining letters 'lette' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'with' is the link.
Can you help me to learn more?
(Other definitions for omelette that I've seen before include "Item of food i" , "Having panned meal" , "Smashed eggs" , "Rope used as lasso" , "Beaten egg dish" .)
