No it's not 'like a parliamentary democracy' at all - the only 'resemblance' is that that there is some degree of 'representation'.

But the similarities end there.

You've actually provided a specific example - the most recent UK election, which highlights even further the lack of democracy in the EU, which is a 'confidence' election based on some important or existential issue, in that case, Brexit.

+ Voters were very well informed that Boris Johnson was to be the PM if a specific party were elected + They were very aware of the general platform of the parties + They were even more aware that the issue at the crux of the election was the type of resolution towards Brexit. + UK elected MPs have tremendous power - demonstrated in that very case: previous to the election, Boris Johnson faced a kind of censure by Parliament several times, MPs of all stripes voting for and against him. + The UK MPs collectively introduced legislation and forced the hand of government on several occasions. + The government was threatened with dissolution on several occasions, over a very important issue.

None of this happens in the EU, by design.

The EU is not a 'representative democracy' rather, it's a political entity which governs largely unto it's own devices - but in which some actions must have it's actions approved by elected officials.