Since you'd gone with 30%, I was assuming you'd exaggerated the US pay gap rather than the EU one. Until I hit your link I was ready to pull out an old DoL report that did a multivariate analysis and ended up with a remaining unexplained gap small enough that it was within margin of error.

Doing some brief reading on the EU numbers from the link you provided I notice a demonstration of one of the things I was getting at - the EU number is much smaller than the US number because the EU number is hourly rather than total and thus mitigates differences in hours worked (since it is average gross hourly earnings it doesn't fully account for overtime, as overtime is typically paid at a higher rate) right out of the gate.

Another thing it notes that is worth pointing out is that the gap is smaller for young employees, which the link suggests could be due to career interruptions being longer and more frequent for women. The DoL report I mentioned earlier notes this as well for the US, and noted it as a pretty major factor - basically the longer and more frequent career interruptions for women on average lead to missed opportunities and small but lasting and cumulative damage to future earnings. Probably the biggest and most straightforward move to adjust this in favor of women would of all things be to expand parental leave for fathers in such a way that men are incentivized to make full use of it, which would significantly reduce the gap in number and length of career interruptions.

An article linked off that page suggests about 20% of the EU wage gap (~3% of the ~14% gap from the year the analysis was done) can be explained by factors they consider in their analysis, which is less thorough than the old DoL one as far as confounding factors and which they admit doesn't include all explanatory factors because the data needed simply isn't available. It's also all over the place when looking at individual EU countries as opposed to the EU average, which suggests that differences in culture and law between various EU countries probably plays a much bigger role than anything else.

Which brings me back to the whole "wage gap don't real" thing - women are not being paid dramatically less than men for doing the same work just because they are women, all else being equal. In no small part because all else isn't equal, and the more you try to account for that, the smaller the gap becomes (except apparently in Luxembourg and Romania, where it goes radically the other direction).