If you are EU based however, as of April 2015, you will need a current EASA licence to go with your FAA one flying an N-reg based in the EU.
EU 216/2008, the reference I presume Steak and Kidney Pie alludes to, certainly does
not refer to the residence of the pilot, or even where [B]he or she[B] is "based." The legislative text is very clear and makes reference to the residence of the OPERATOR. The word "base" does not feature in the text of the legislation.
Also, you cannot "convert" your FAA license to an IOM one. IOM do not issue licenses, they merely validate ICAO licenses.