Make it so that:
1. Ottomans conquer Persia (at least the territory of modern day Iran + Greater Iran possibly)
2. They do it before a significant part of the population manages to convert to Shiism
3. They keep it long term and cost of garrisoning it is not higher than taxes collected from it and military recruits gained from it (i.e. it is a net benefit to the Ottoman state)
Malkoçoğlu Turali bey kills Ismail in field personally. According to legends they faced each other with the latter killing the former by slicing him in half with one swing. The two Malkoçoğlu brothers died in the battle, that we are certain.
Selim has no issue as the Safavids are now broken in morale. If Ismail's son Tahmasp is also killed even better. The whole Qizilbash rallying around the head of the Safaviyya Order is gone.
Their conquest of Persia collapses. The Ottomans move further from Tabriz to Qazvin, Qom, Kashan and maybe even Esfahan only to return to Mesopotamia to Baghdad.
Selim grants some dissatisfied Turkmens of Anatolia with Beyliks in Persia on the condition that they remain Sunni and do not join with Shia's. Over a period of time most of Persia with an exception of Khorasan and Baluchistan is nominally Ottoman, though ruled by hereditary beyliks.
The situation is: Azerbaijan, Khuzestan and Iranian Kurdistan is under Ottoman administration. Inner Persia is ruled by various Turkmen and Persian nobles with hereditary rulership there... areas as East as Golestan, Kerman, Bandar Abbas (does not exist in TTL but I use it for the sake of clearing the area) are nominally Ottoman. But the situation is comparable with the Ottoman Maghreb, do it may evolve into Ottoman Egypt over time.
The Ottomans either need hereditary divided Beyliks in Persia to guarantee control or one strong beylik with a governoe, like in Egypt with more freedom to face Eastern Threats. The risk of the governor breaking away like Mehmed Ali is also likely. It is a wealthy place, large, far away from Constantinople and Geographically harder to control than Egypt.
This situation is prior to the conversion to Shiism by the Safavids. Zaidi and Ismaili minorities still exist though. The Ottomans will have minimum men for garrisoning duties as my expectation is that the local autonomous beyliks will use their own manpower for Eastern skirmishers. Twelver Shiism is curbed massively. Azerbaijan will be economically more tied to Anatolia. Less decline of Turkmens in Eastern Anatolia as there is no lomger a reason to suspect their loyalty.
Realistically speaking, the Ottomans cannot directly control Persia until the age of the railroads. Until then, the situation is either A). Ottoman Maghreb though closer tied to the capital unlike the Maghreb or B). Ottoman Egypt with some old institutions kept intact to rule the area with local nobles (Mamluks in Egypt etc + more freedom for the governor).