Former sheep I make into cold meat (8)

I believe the answer is:

pastrami

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

'meat' is the definition.
(I know that pastrami is a type of meat)

'former sheep i' is the wordplay.
'former' becomes 'past' (similar in meaning).
'sheep' becomes 'ram' (male sheep).
'past'+'ram'+'i'='PASTRAMI'

'make into cold' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for pastrami that I've seen before include "Smoked, highly-seasoned cut of beef" , "A tramp is (anag) - meat" , "Spiced sliced beef" , "Sliced cured beef" , "Seasoned dish" .)

I've seen this clue in the Sydney Morning Herald.

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