Using any reasonable PoD after the Iran Hostage Crisis, restore good relations between the United States and Iran. Bonus points for moving up from friendship to alliance.
By 1992 Iranian forces are rebuilding Baghdad and absorb Turmenistan, Azerbaijan, and have mended relations with America. Tehran settles down as foreign capital comes back into the nation and the 1990s see radical leaps in standard of living. The 09/11 saga solidifies the new friendships/de facto alliance against radical Sunni Islam between Tehran and Washington as the Taliban are mowed down by Iranian forces already on the verge of war with them. Northern Iraq becomes an autonomous state as the rest melds into Iran and much of world's attention focuses on North Korea over the next few years.
I never understood all this stuff about Iran annexing large areas outside its borders. Iran may see itself as a Shiite state, but it also sees itself as an Iranian (ethnic) state. Neither the Turkmen, Azeris nor Marsh Arabs are Iranians, and Tehran already has enough troubles with minorities.
Annexations are old-fashioned in most places, it's far easier to just have friendly governments where you need them. Did the US annex Western Europe after WWII? Did it need to? All the Iranians will accomplish is greatly piss off the Russians, Arabs, Turks, remaining Central Asians, Afghans, and Armenians, maybe even the Pakistanis (certainly the Israelis, but that makes little difference), all while losing the ethnic majority in their own country and having it replaced with a simple plurality.
Oh, and the Turkmen aren't even Shiites.
Azeris not Iranian? Try telling that to Ayatollah Ali Khamenei.
To say Iranian is ethnicity would be like saying Roman, in the context of the classical empire, was an ethnicity. It of course wasn't. Similarly, Iran has always been a multiethnic transnational state, and to claim otherwise is clearly untrue.
And there are already Turkmen Iranians, who follow Sunni Islam, like 8% of their fellow Iranians. To suggest that Iran is solely Shi'a is another brash over-simplification.
To meet the U.S. concern about an Iranian nuclear weapons program, the document offered to accept much tighter controls by the International Atomic Energy Agency (IAEA) in exchange for “full access to peaceful nuclear technology.” It proposed “full transparency for security [assurance] that there are no Iranian endeavors to develop or possess WMD” and “full cooperation with IAEA based on Iranian adoption of all relevant instruments (93+2 and all further IAEA protocols).” That was a reference to new IAEA protocols that would guarantee the IAEA access to any facility, whether declared or undeclared, on short notice -- something Iran had been urged to adopt but was resisting in the hope of getting something in return. The adoption of those protocols would have made it significantly more difficult for Iran to carry on a secret nuclear program without the risk of being caught.
The Iranian proposal also offered a sweeping reorientation of Iranian policy toward Israel. In the past, Iran had attacked those Arab governments that had supported the Israeli-Palestinian peace process, and Tehran had supported armed groups that opposed it. But the document offered “acceptance of the Arab League Beirut declaration (Saudi initiative, two-states approach).” The March 2002 declaration had embraced the land-for-peace principle and a comprehensive peace with Israel in return for Israel’s withdrawal to 1967 lines. That position would have aligned Iran’s policy with that of the moderate Arab regimes.
The document also offered a “stop of any material support to Palestinian opposition groups (Hamas, Jihad, etc.) from Iranian territory” and “pressure on these organizations to stop violent actions against civilians within borders of 1967.” Finally it proposed “action on Hizbollah to become a mere political organization within Lebanon.” That package of proposals was a clear bid for removal of Iran from the list of state sponsors of terrorism.