Quark cheese, hardly any remaining from the first minute (5)

I believe the answer is:

charm

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'quark' is the definition.
(charm quark is a kind of quark)

I can't explain the remainder of the clue.

(Other definitions for charm that I've seen before include "For example, olde-worlde character" , "Something believed to bring good luck" , "Enchant" , "Group of goldfinches" , "Make delighted" .)

I've seen this clue in The Guardian.

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