Gradually deplete Spanish red with creamy centre (3,4)

I believe the answer is:

eat into

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'gradually deplete' is the definition.
(I've seen this in another clue)

'spanish red with creamy centre' is the wordplay.
'spanish red' becomes 'tinto' (I am not sure about this - if you are sure you should believe this answer much more).
'with' is a charade indicator (letters next to each other).
'centre' says to take the centre.
The central letters of 'creamy' are 'ea'.
'tinto' put after 'ea' is 'EAT INTO'.

Can you help me to learn more?

(Other definitions for eat into that I've seen before include "Corrode (something)" , "run down" , "start wearing out" , "Consume (resources)" , "Etch" .)

I've seen this clue in The Irish Times.

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