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Minister is missing old friend in Paris providing choice from the deli (8)

Ross

I believe the answer is:

pastrami

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

'choice from the deli' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.

'minister is missing old friend in paris' is the wordplay.
I cannot quite understand how this works, but
'old' could be 'past' (similar in meaning) and 'past' is found within the answer.
'friend' could be 'ami' ('friend' in French) and 'ami' is found in the answer.
A single letter 'r' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

'providing' is the link.

Can you help me to learn more?

(Other definitions for pastrami that I've seen before include "A tramp is (anag) - meat" , "Meat dish" , "smoked joint" , "beef dish" , "Smoked, highly-seasoned cut of beef" .)

I've seen this clue in the Irish Times (Crosaire) and The Irish Times.
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