New built since when and by whom?

By almost everyone since almost a decade.

Spain has designed and built Juan Carlos I.

Australia will buy two slighty modified BPE (i.e. Juan Carlos I).

France as built two Mistrals, is building a third Mistral, maybe will build a fourth one too.

Japan has built in the near past three LSD LCAC-capable, Osumi class.

South Korea has built Dokdo.

Italy is planning between two and three LHD, rumors got their dock should be LCAC capable (meaning U.S. LCAC 1, of course).

Every of the above mentioned classes has a dock compatible with U.S. built LCAC 1.

The last amphibious class designed in western countries lacking a dock LCAC capable seems to be the Rotterdam-Galicia-Bay family, designed in the early nineties.