Earlier quoted context omitted.
EU is as democratic as your average EU country. Or have you skipped voting in the EU elections?
How do EU parliament elections help you choose the EU commission members? In your average EU country the elected parliament chooses the government. Not in EU.
In the EU it works exactly the same: you vote for a party, which has a vote on accepting or rejecting the proposal for the current proposed commission (where there has to be 1 nominee from each member state and is handpicked by the council of European Union, i.e. your ELECTED state ministers)[1][2].
Can the EU become more democratic? Absolutely, but that will be at the expense of EU member state's sovereignty, which is why it looks like it does right now.
[1]https://en.wikipedia.org/wiki/European_Commission
[2]https://en.wikipedia.org/wiki/Council_of_the_European_Union#...