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Eat out in La Gavroche, and see who's inside? (4)

Ross

I believe the answer is:

etch

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'eat out' is the definition.
(I've seen this before)

'gavroche and see who's inside?' is the wordplay.
'gavroche' becomes 'etc' (I can't explain this - if you can you should believe this answer much more).
'and' says to put letters next to each other.
'inside?' says to take the centre (I've seen 'inside' mean this).
The central letter of 'who' is 'h'.
'etc'+'h'='ETCH'

'in la' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for etch that I've seen before include "Make picture by engraving metal" , "Carve (design) on a surface" , "Engrave (metal, glass etc.)" , "Use acid to design on metal or glass" , "Make designs" .)

I've seen this clue in The Telegraph.
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