Cold food consumed like a baby (10)

I believe the answer is:

childishly

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'like a baby' is the definition.
I can't tell whether this defines the answer.

'cold food consumed' is the wordplay.
'cold' becomes 'chilly' (I've seen this before).
'food' becomes 'dish' (dish is a kind of food).
'consumed' indicates putting letters inside.
'chilly' placed around 'dish' is 'CHILDISHLY'.

Can you help me to learn more?

(Other definitions for childishly that I've seen before include "Like baby" , "In an immature fashion" , "in puerile manner" .)

I've seen this clue in The Globe and Mail.

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