I spent some time looking into it. Quoting a customer in Europe 1 price (pre-VAT) and then they need to figure out how to pay the extra VAT separately didn't sit well with me. So I want to figure out a way where the customer wouldn't get a 2nd bill when his shirt arrives. This started to get complicated, so I unfortunately have not been able to get to the bottom of it yet.
If you have any advice on how to ship to EU and pay the taxes on my end (so the customer doesn't pay something separately), please let me know!