This is nonsense: the commissioners are not a self-appointed oligarchy. They are appointed by the European Council, that is to say by the head of all EU states. It is called indirect democracy, and is certainly not anti-democratic by any stretch of the imagination. If you don't like the EU commissioners, the fault resides solely on whoever we (European citizens) collectively picked as a our respective head of states (in my case that would be François Hollande, the French president).

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