We just call it a toast without any country affiliation. And it’s not sweet, it’s savory. You make it with the same egg and milk mixture, but with a pinch of salt (no pepper).
And in my opinion – much better. Not only because we all eat too much sugar and I would rather save my sugar consumption for some special dessert. It’s more versatile with slice of ham or cheese on top, can be done with any stale bread, not necessarily challah of brioche (just needs to be soaked in eggs and milk mixture longer), very satisfying and can be eaten with fingers.
Love the ham and cheese idea!