Kind of door finished twice? (2-3-4)
I believe the answer is:
'kind of door finished twice?' is the definition.
I can't judge whether this defines the answer.
'finished twice?' is the wordplay.
'finished' becomes 'up' (eg 'time's up' means the time is finished).
'twice?' becomes 'andover' (I am not sure about this - if you are sure you should believe this answer much more).
(Another definition for up-and-over that I've seen is "(Of door) rising into horizontal position".)