YDG (tacky name
, well done!). In exactly the same way as employment is restricted in the US to those with a Green Card and the appropriate professional qualifications, in the EU you
must have the right to live and work here, and you must have a JAA professional pilot's qualification (CPL or ATPL).
The right to live and work here requires that you are either an EU citizen, or that you are eligible for EU citizenship through birth
ie one or both of your parents are EU citizens. In certain countries of the EU there may be a slightly more liberal interpretation of this rule - but not much! If you're not sure, check with the Consulate or Embassy of the EU nation which you think you may be eligible for nationality of.
Once you have established the right to live and work here, you must obtain the JAA CPL or ATPL. The conversion from the FAA equivalent is not easy or straightforward, but has been covered here before so please search using something like 'FAA to JAA conversion' - you should find it. Alternatively, you can research the requirements on the CAA's website (
here, I think!) yourself.
Your degree and engineering experience are less important than your flying experience - unlike the USA, degrees are not required of pilots. Whether easyJet would be interested in you can only be established by you contacting easyJet, I'm afraid! Similarly for any other EU airline.
Best of luck.
Scroggs