One more try......... As I have already explained, Melancholy, the 28 European Commissioners (soon to be 27, sadly) are each appointed (or "appointed" if you prefer ;-) by the democratically elected government of their own member state. The commissioners propose legislation to the elected EU parliament, which considers it and approves it (or not).
In the UK, the equivalents of EU Commissioners are our Ministers of the Crown, who are also appointed, in their case by our unelected monarch, on the recommendation of our elected Prime Minister. Ministers propose legislation to the UK parliament, which considers it and approves it (or not).
They are slightly different processes but they are both undoubtedly democratic. If there is one that is more democratic than the other, it is the EU procedure, because the decisions of the EU Parliament cannot be changed by an unelected upper chamber.
But the EP's decisions are on proposals made by an unelected executive. We keep coming back to this, don't we?
And who are the commissioners accountable to? Can they be voted out if the public don't like the laws that they propose? Can their directives that become law be repealed by the member countries once they've been enacted? Do tell.
We certainly know that in this country an unpopular government (that's the Prime Minister and Ministers of the Crown) can rightly be booted unceremoniously out within 24 hours of votes being cast, whilst pretty much any UK law could be repealed at a stroke if a new government with a mandate so wished. Thankfully past EU laws can now be repealed after Article 50 was triggered. Though any government with the actual spine to do this is unlikely.
And you shouldn't try and distort the nature of UK's parliamentary democracy by trying to infer that the Queen's position is anything other than ceremonial. I'd invite you to specify the last time she refused to appoint a Minister to Government (clue - you won't be able to because she hasn't).
Quite apart from all this, we haven't even begun to discuss the actual practical effect of the EU's wonderful democracy at work. So it can transpire that an unelected commissioner from that great farming island of Malta could have equal influence on the formulation and outcome of UK agricultural law than our own unelected UK commissioner, and the votes of the Luxembourgian and Lithuanian people (all in huge turnouts of course :-)) can elect EU members of Parliament to vote it through.
Did I mention Malta? Ah yes, the curiosity of the European Parliament which decides how many seats a country can get. Malta has 6 MEPs from an electorate of 340,000. The UK has 73 MEPs from an electorate of 47,500,000. Which essentially means that Maltese voters have over 10 times more power than UK voters. Democratic? You decide.
And let's not even mention the great British Remainer public that's so passionate and engaged about the EU that the last European elections to be held before the referendum bagged a whopping 35.6% turnout, all under a PR system where every vote counts. In fact, the entire turnout of that vote would still have lost the referendum even if they'd all voted Remain. Though when you consider that UKIP was the biggest party that seems remote!
Let's get back to good old fashioned Parliamentary sovereignty. Any step there is in the right direction.