Crossword Genius

Lay it on thick like Hollandaise at brunch (7)

Ross

I believe the answer is:

overegg

I'm a little stuck... Click here to teach me more about this clue!

'lay it' is the definition.
I know nothing about this answer so I can't tell whether this works.

'on thick like hollandaise at brunch' is the wordplay.
I cannot quite understand how this works, but
'on' could be 'over' (over can mean on top of) and 'over' is present in the answer.
'like' could be 'eg' (I've seen this in other clues) and 'eg' is found in the answer.
A single letter 'g' remains 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 overegg that I've seen before include "Something to do with pudding" , "Embellish unreasonably" , "Hugely exaggerate" .)

I've seen this clue in The Independent.
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