Ideally miss the middle parts of Top Hat (2,1,1)

'ideally' is the definition.
Both the answer and definition are adverbs. Maybe you can see an association between them that I can't see?

'miss the middle parts of top hat' is the wordplay.
'miss the middle' becomes 't' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'parts' indicates taking the first letters (I've seen 'part' mean this).
'top' means to remove the first letter.
The initial letter of 'of' is 'o'.
'hat' with its first letter taken off is 'at'.
't'+'o'+'at'='TO A T'

Can you help me to learn more?