Suppose Hitler, for any one of a number of reasons, goes into a coma June 1, 1941, and at least seems to make a complete recovery a little over two months later?
On December 1, 1941 he has a relapse, and he goes into a coma and does make a complete recovery five weeks later?
What difference does it make?
Goering assumes power. However, there is an immediate ferment of intrigues among the remaining Nazi leaders.
Goering was opposed to the invasion of the USSR, but went along with Hitler (as he always did).
If he comes to power before the invasion, IMO he cancels or suspends it. His excuse may be that only the "true" Fuhrer has the right to commit Germany to such a colossal enterprise, and that without Hitler's leadership, it should not be attempted.
He may try to negotiate peace with Britain. When rebuffed, he may resume the Blitz. I don't know how he felt about the war in Africa, but he might decide to reinforce Rommel, and thus put more pressure on Britain.
Both of these actions would take some time, and Goering would not presume to take them immediately, so they would come into effect in mid-July, and be just started when Hitler wakes up.
Hitler may be annoyed that BARBAROSSA has not gone forward, but I suspect he would accept Goering's flattering excuses. He would then order BARBAROSSA for mid-August - allowing a week or two for final prep. I'm pretty sure he believed BARBAROSSA would succeed within two or three months, so he would not consider August too late to start it.
The big question at this point is what Stalin is now thinking. He said there would be no invasion, and there wasn't - but Hitler's illness figures into that. The mountain of intelligence about German preparations only got bigger. Still, Stalin may remain obdurate.
Soviet preparations will be about two months further along, which will help somewhat.
That's the situation. BARBAROSSA starts on say 15 August. It goes more or less as OTL, though slightly better for the more prepared Soviets. However, the fall rains set in after two months. This prevents the Axis from closing the Kiev pocket, invading the Crimea, and isolating Leningrad.
When the ground freezes in mid-November, the Germans attack again. This is against the Vyazma-Mozhaisk position west of Moscow. OTL the Germans blew through it in early October, and took over 600,000 prisoners. But in freezing weather, it won't be so good. The Germans will make several penetrations and cause much damage, but they won't break through or get near Moscow.
When Hitler collapse again on 1 December, Goering will again take over. Soviet counterattacks will begin about that time, and Goering - unlike Hitler - will authorize withdrawals.
Soviet casualties will be about 1.5 million less, with that much more strength for the winter counterattack. Between that and German withdrawals, the front will be moved west 300 km, to the Dnieper.
Hitler will reawaken in January, and this time he may be angry enough to sack Goering.
What else? Well, if the Pacific War develops on OTL's schedule (and why not?), then it is up to Goering whether Germany declares war on the U.S. I think, as before, Goering delays - again deferring to Hitler when he wakes up. When he does, I think he declares war. This has various knock-ons for the Battle of the Atlantic.