Pretty simple, but Andronikos III Palaiologos doesn't die prematurely of Malaria. This averts the Byzantine Civil War of the 1340s, enabling John Kantakouzenos to complete the reunification of Greece under the Roman auspices and stave off any Serbian adventures against the Empire until the Black Plague hits. Andronikos dies then, but instead of leaving his son as a nine year as OTL, his death now leaves him on the cusp of 16, avoiding the question of the Regency. Against the coalition of Anna of Savoy, the Patriarch John XIV Kalekas and Alexios Apokaukos, Kantakouzenos loses out in influence to the reformers and the Empire begins a new golden age of reforms, by embracing commerce and an empowering of the Imperial state structures, in effect a return to the Macedonian dynasty's policy that resulted in a quasi-meritocracy.
Although kicked out of Anatolia by this point, the Empire is able to consolidate and come to hold all the territory below the Balkan Mountains and, in a matter similar to France in the early modern area, enforce a policy of Romanization that binds these territories to it. Taking a cue from the Italian merchant republics, the Empire makes up for its lack of taxable land by translating its strategic location at the crossroads of Asia and Europe to utilize commerce as a new money maker. Using a combination of hard and soft power, the Byzantines pursue a policy of preventing any one Turkish polity of controlling Anatolia, forging alliances as needed to cripple threatening powers; the Ottomans are crushed in this manner in the 1370s. Ultimately, the Byzantines aid the rise of Russia by curtailing the slave trade in the Black Sea ran by the Tartars and using their formidable navy in conflicts against them, helping the Russians to secure control of the Steppe sooner and enforce Christianization. The crowning achieve of this new Byzantium comes in the early 1500s, when they conquer Egypt from the decaying Mamelukes.