At least in BE we talk about the Middle East, not the Mid-East, and about middle-eastern countries. (The Mid-East sounds as if it should be somewhere in the US, since the Mid-West certainly is.)
By the way, Wikipedia lists the following countries in connection with the practice of stoning: Afghanistan, Indonesia, Iraq, Iran, Mali, Nigeria, Pakistan, Saudi Arabia, Sudan and Somalia, whereas Bahrain, Egypt, Iran, Iraq, Israel, Jordan, Kuwait, Lebanon, Oman, Palestine, Qatar, Saudi Arabia, Syria, Turkey, the United Arab Emirates and Yemen are said to be middle-eastern countries. Not so much overlap there. Referring to The Greater Middle East brings in Afghanistan, Pakistan, Somalia and Sudan, but also another 15 countries e.g. Georgia which might not be too happy to be associated with stoning!