I have read some very compelling posts that while capturing the oil fields would had been to hard and of no benefit to Germany, they could had captured the USSR breadbasket in the Kuban and Ukraine, which would had eventually caused a famine that would had made the USSR unable to continue fighting.
So what if instead of going for the oil fields, Hitler and the high command recognized this and went for a strategy of capturing the Kuban and relevant regions, then fortify defenses in those areas and camp there until starvation set in (I assume around 2 years) and have the USSR capitulate or easily crush a starving Red Army?
Problem is the Germans already captured the Ukraine and chunks of the Kuban? Great chunks of Soviet agriculture was seized (or burned in scorched earth retreats anyway) Russia already suffered food shortages and stringent rationing OTL.
An oddity here is that an awful lot of people the Soviet Gov had been responsible for feeding in June 1940 were now out of their area of control anyway being under German occupation. This wasn't much comfort for those people of course since the occupiers had 0% interest in feeding them (actually the opposite was a matter of intentional policy) but it was less people the soviet government had to feed in the short term. This works both ways of course one of the most chronic points of food shortage for Russia was 1944 -1945 when they were not only fielding a huge army, had been suffering for a couple of years accumulated food shortage and now suddenly taking back large amounts of territory which contained 10m's of very hungry Russians!
As pointed out LL already made food a big thing,
But your plan's issue is you've just given the soviets what they need, namely time.
In two years the Soviets will build, equip, train and concentrate their much greater numbers. The Germans can dig in sure, but stuck thousands of KM at the end of their already massively strained logistics chain fortifying in a big way is going to be tough (it'd not like the Soviets will just leave them alone either but will now be able to pick and choose when to mess with them).
Basically the Germans are screwed either way, but this is giving up the initiative.
Also the Germans need that oil, the fact that we know they had pretty close to zero change of actually getting much of it back in time to matter even if they had taken the fields doesn't change that.