The Mille Crepe ("mille" means "thousand," which refers to the dessert's many layers of crepe) features thin crepes layered with cream ("melting cream" according to the brand's website). It's a classic French dessert. There looks to be about 7 layers of creme and 8 layers of crepes in Domino's version.
The Mille Crepe is available through January 2016 for 980 yen (~$7.96 US) per order.
Photo via Domino's Japan.