“We are a people who do not eat until we are hungry. And if we eat, we do not eat to our fill.” Is this an authentic hadith?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

What you have mentioned in the question is not a Hadeeth of the Prophet and it does not exist in the books of Sunnah and its registers.

The author of As-Seerah Al-Halabiyyah mentioned it without stating any chain of narrators, saying: "Some said that Al-Muqawqis sent a doctor with the gift to the Prophet who said: 'Go back to your people. We are a people who do not eat until we are hungry. And when we eat, we do not eat to our fill.'" [End of quote]

Al-Albaani said about it in his book As-Silsilah As-Saheehah (7/1651 -1652): "There is no basis for it."

Allah knows best.