If then the push for oil was that imperative Case Blue being launched by the pre-battle plan would take them easily to Stalingrad by the end of July, more likely that not taking the city before the defenders could get defenses prepared enough a month later when they got their IOTL. I disagree with 'Nuker about the logistical ability to run 4th Panzer army directly at the city from July 13th on instead of diverting it south. Stalingrad then would most likely have fallen after a quick fight outside of it, rather than a grinding attritional fight inside. Then follow that up with a move into Maykop and once the falls focus on taking the ports along the Black Sea Coast rather than moving on Grozny. Don't keep necessary forces like the Italian Alpine Corps on the Don, send them to the Caucasus. Keep the 11th army with AG-South near the Don as a reserve. Then sit still in 1942 to hold their positions and interdict the Volga.
Otherwise they should not invade Egypt in 1942, instead take Malta. Once that is accomplished then consider moving into Egypt. Once the US lands in Morocco then pulled back to Libya and evacuate to Sicily rather than try to fight in Tunisia. Then with evacuated Italian forces and the Afrika Korps in Sicily, plus with Malta as an outpost invading Sicily is not an option, Greece is not a good option either, which leaves forces the Allies to invade Sardinia or France in 1943. If they go France the US lacks combat experience and a lot of other buffs (the Mulberry Harbors, oil pipeline to Portsmouth) for Normandy, plus the Luftwaffe hasn't yet been destroyed and its a lot easier to use it in France than over Tunisia/Italy to best effect. If my fighter option was chosen in 1942 then there should be more than enough to contest France in 1943 and if there hasn't be the Stalingrad disaster or Tunisian one there is enough left in France to resist an invasion, especially if there is not a Kursk offensive on the table in the East.