A young MOngol boy named Temujin, and his family are basically made outcasts from the safety of his tribe, and begin to wander the fringes of the nomadic Mongol areas.
During this time of trial, he meets a Buddhist monk who aids both he and his family, and as a result, Temujin begins to feel some identification with the Buddha, particularly when he learns of his noble birth and subsequent wanderings.
But this new found identification with Buddha proves to be only a veneer on the young mongol boy, and as he fights his way to the top of his tribe, his perspective on these teachings changes. He comes to believe that the conqueror is a valid ncarnation and step to a balanced state of being. In other words, he sees himself as a sort of buddha with attitude.
Shamans and religious hoaxsters are able over the years, develop a sort of core set of mongol buddhist beliefs that are consistent with Temujin's personal beliefs.
Through a combination of adroit political moves and strong arm tactics, Temujin is declared Genghis Khan in 1206 by other Mongol chieftains. Since his brand of Buddhism includes the Conqueror as a valid incarnation of Buddha, his position soon also has taken on many religious aspects.
He determines to bring his brand of Buddhism to the world, and in this TL his conquests mirror those of OTL. Originally seeking to conquer China he eventually turns to easier 'pickings' and expands into the West, conquering the Uzbeks and many Turks, forceably converting them to Buddhism.
Finally his hordes careen into the growing Orthodox and Mithric areas of our Russias and the Baltics where, in a stunning series of battles, the mongol hordes are held but not defeated, first by the byzantine Orthodox, and then by a smaller but very well disciplined Mithric force made up of soldiers from throughout Europe.
Unfortunately, by the time the dust settles on all this, Persia and several other Kingdoms have fallen to the Brutal forces of Buddha.