Those "several hours" are 500, then one will get an unrestricted endorsement. If it is less than that, the endorsement will be restricted to US-registered aircraft. As those four (respectively six) landings are an integral part of the type rating, an EASA-certified TRI has to "teach" you how to land the aircraft - "learning by doing" does not suffice.
I heard of someone who did the course and did check flights under EASA and FAA and after several hours on type with FAA License he applied to UK with the EASA check form with proof that landings had been done by virtue of FAA license flights and was given the endorsement.