Can't we just have them do something smart for a change. Barbarossa was started with too few mobile forces, something that was accepted on the basis of faulty intelligence estimates both of Soviet strength and stability. The Germans could do the math, and realise that now that they had a lot of allies (Hungary, Romania, etc) they could improve the strength of axis forces at a faster ratio than the USSR. In one year, with a proper production plan and an ambitious and well coordinated training effort, the axis could field more mobile forces, and the fighting power of its allies could be dramatically improved. The Soviets would be improving also, but they were at the initial stages of introducing new types of everything, having made a vast investment in the mid 30s on now obsolete equipment. So the ratio of progress could favour the axis.
By mid 42, if the German were smart, they could have the same amount of mechanised forces, but with PzIVF2 as standard (just pull back OTL production one year and that gives you the c2000 tanks needed) but critically they could cascade equipment (PzIII, Pz38, Somuas) to their allies so that the Hungarians, Romanians and Italians could each provide an extra PzK, trained to near German standards.
Quality ratios would still favour the Germans (the Bf109F and FW190G were still superior to the Yak 1s, they would face,etc).
The critical factor would be which side uses the extra year better to improve its starting situation. But the fact is that with proper intel, anyone could have understood at OKW that they were one PzG and a few Army Corps short for OTL Barbarossa.