ITTL, Tunisia is secured during Op. Torch, perhaps by increased Vichy cooperation, meaning the flaws in the US Army are not exposed. Also, the Axis is spared the loss of ~360k men, 3k aircraft, 1k guns and ~450 tanks (minus whatever made up the original Panzerarmee Afrika that retreated into Tunisia OTL, and which is mostly lost ITTL as well).
The Allies then invade Pantelleria, which works, followed by Sicily, which doesn't. Exactly why the landing failed is not really important, but let's call it a mix of Allied screw-ups and increased Axis numbers plus flawless maneuvering/positioning. (Yes, I know it's unlikely, and the Allies would have picked another target if they knew Sicily to be too heavily defended, but lets just go with it)
At the same time the Sicily landings are underway but before the decisive axis counterattack, Turkey decides to join the Allies by declaring war on Germany (but not Bulgaria, the only axis member it shares a border with). To their horror, the allied landing is repelled. (I know Turkey had no real reason to join the Allies at this point, but let's just accept the premise ok? It's just a fun little thought exercise, nothing serious)
How do things progress from here? Can the Allies clear the Aegean in time?