The EU has an elected Parliament but one of they key complaints about the EU is that the Parliament has extremely limited power while the bureaucracy of the EU ends up making most of the rules.

As an obvious case in point, the EU Parliament has no authority to propose legislation.  All legislation has to originate from the European Commission which is an unelected body.  The EU Parliament can approve or decline that legislation, but can't really do much else.

Ohh, and the appointment of members of the European Commission?  That is handled by the Council of the European Union, which is ANOTHER unelected body, essentially like the Senate of the EU, being appointed by the executive of the member countries.

To say that the power of the EU Parliament is muted would be an understatement.