How very dare you!?
As a catchphrase this will likely have more than one meaning - deliberately. The obvious sense to me is that 'very' emphasises just how much the speaker feels outraged. 'How' on it's own is insufficient. 'Very' is modifying 'how', making it 'bigger' as in (paraphrase) -
Do you have any idea how much I feel you are overstepping the line?
This is obviously, simultaneously, exclamatory and interrogative.