I'm not sure that understanding how the EU Commission and Parliament relate to each other will help convince people the EU is democractic. In particular, the president of the European Commission is currently chosen by some really weird ostensibly-democratic insider political trading: https://www.politico.eu/article/spitzenkandidat-jean-claude-...
Well, again, the directly voted European Parliament 1. elects the President of the Commission, 2. acks/nacks the contents of the Commission and 3. can force the Commission to resign.
I mean, it's not like a wink, wink, handshake and some random person gets installed just like that as the President of the European Commission.
The Parliament really has to approve the person, whoever it is and however the person is found.