Challenge LA tourist eating Italian ice (6)

I believe the answer is:

gelato

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

'italian ice' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'challenge la tourist eating' is the wordplay.
'eating' indicates the answer is hidden within the clue.
'GELATO' can be found hidden inside 'challenge la tourist'.

Can you help me to learn more?

(Other definitions for gelato that I've seen before include "Italian ice cream" , "treat in Milan?" , "Frozen food" , "Italian-style ice cream" .)

I've seen this clue in The Times.

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