。
Was it you who left the door open last night?
Literal
Last-night door [object-を] leave-open-[nominal-のは] you is-[polite-ですか]?
A cleft construction — Japanese uses [clause]-のは [noun]です to create 'the one who did X is Y.' 開けっ放し combines 開ける ('open') with the suffix ~っぱなし ('leaving [something] in a state'), giving 'left open.' The ~っぱなし suffix is productive and useful: 出しっぱなし (left out), つけっぱなし (left on), 言いっぱなし (said and done with, unretracted). Slight accusatory cadence in the question.