The EU is not a democratic entity by any stretch of the imagination, it is anti-democratic, over-ruling elected members and overriding the wishes of the people.
Don't get me wrong: I would prefer for the EU commission to be elected more directly by the European citizens. And I certainly wish that the European parliament had more power. But keep in mind that the only reason it's not happening is because the various EU governments don't want to give up too much power: they have full control of the EU commission, but not of the EU parliament / EU citizens...
TL;DR: power in the EU is held by the European Council, that is to say by the head of states.
EDIT: typo
And how exactly are we going to hold the head of states accountable, so one could say we control him/her?
(Brexit - the movie). Sure, it's supporting Leave but the factual evidence is, well, just fact.