Most difficult beginning to miss the peak (7)

I believe the answer is:

everest

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

'the peak' is the definition.
(Everest is an example)

'most difficult beginning to' is the wordplay.
'most' means to remove the first letter.
'difficult' becomes 'severe' (I've seen this before).
'beginning to' becomes 'st' (I can't justify this - if you can you should believe this answer much more).
'severe' with its initial letter taken off is 'evere'.
'evere'+'st'='EVEREST'

'miss' is the link.
I am not very happy about this link. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for everest that I've seen before include "High mountain" , "A high spot" , "Mountain named after a British surveyor general of India" , "Tallest mountain ..." , "The world's highest mountain" .)

I've seen this clue in The Hindu.

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