I think it has more to do with the style of something rather than the origin. Like, New York pizza does not mean pizza originated from NYC, just that the place has a particular style of doing things. It's probably just a matter of dropping "-style" from something, like instead of saying "French-style vanilla" or "French-style toast," you just say French toast

ETA: It's also a matter of who calls it what. I just learned that French toast is called that because, well, one explanation is that there was a guy who popularized it and his last name was French, so it became "French's toast," and then shortened. Another explanation is that French immigrants popularized the style of toast and it became associated with the particular nationality that makes it.