They say I shout loudly for something very sweet (3,5)

I believe the answer is:

ice cream

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'sweet' is the definition.
(ice cream is a kind of sweet)

I don't understand how the rest of the clue works.

(Other definitions for ice cream that I've seen before include "Cold dessert" , "Frozen food made with milk fat" , "Cool confection, sweet frozen dessert" , "Sweet frozen food" , "Gelato-like dessert" .)

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

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