Relating to food that's good, in a big way (15)

I believe the answer is:

gastronomically

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

'good in a big way' is the definition.
The definition suggests an adverb which matches the answer.

'relating to food that's' is the wordplay.
'relating to food' becomes 'gastronomic' (I've seen this in another clue).
'that' becomes 'ally' (I can't explain this - if you can you should give a lot more credence to this answer).
'gastronomic'+'ally'='GASTRONOMICALLY'

Can you help me to learn more?

I've seen this clue in The Telegraph.

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