A recent post at Language Log discussed a South Korean effort to change the ideograms used to represent Kimchee, the Korean national dish, in Chinese.
One of my comments, and follow up to it (some by people much more knowledgeable about the subject than I), discussed the history of this dish and other famous national dishes. I recap the pertinent posts below:
Kumara probably left South American a century or more before it arrived in New Zealand.
Of course, not all signature foods are recent. For example, curry has been eaten in the Indus River Valley since the pre-Indo-Aryan Harappan era.
Also, vaguely on point, the pre-historic hunter-gatherer population of Morocco had very high rates of tooth decay, probably due to a very carb-heavy diet of sweet acorns and snails. The acorns were likely boiled and also likely made into flours, a good reminder of the fact that flour is much, much older than grain domestication.