Ultimo Dragon as Yoshihiro Asai hits an Asai Moonsault (via UltimoDragonAttitude)
Innovated by Ultimo Dragon (Yoshihiro Asai), the move is a variation on the standard moonsault backfliip press of splash. From outside the ring, the attacker will springboard off the middle rope onto an opponent on the floor. Above is the classic Asai Moonsault.
The "Asai Moonsault" in the broader sense is any springboard moonsault to the outside. Below is Naomichi Marufuji hitting a glorious one on Jushin "Thunger" Liger. Dig the hesitation on the top rope.
Asai Moonsault (via AJPWrestling)