By December 1941 the German advance had stalled at the gates of Moscow (advanced German reconaissance units were supposed to have been close enough to Moscow to see the spires of the Kremlin in their field-glasses).
Much German effort and resources were expended in 1941-1942 in subduing the Crimean peninsula and Black Sea area. Mostly i think it was solely for geographic reasons - Hitler was determined to keep the Russians out of bomber range of the vital oil fields at Ploesti, in Rumania. In 1942, Manstein led German forces in operation "Bustard Hunt" in a massive, and succesful, campaign to drive the Russians out of the Crimean peninsula, including the huge fortress at Sevastapol. Immediately thereafter Hitler made the (bad) decision to split his forces, sending half rumbling toward Stalingrad, and the others toward the Caucases oil fields - the farthest east Hitler would ever get.

My question is, do you think it would be feasible, advantageous, or military practical, for Hitler to have avoided being bogged down in the Crimea in 1941-42 by moving east far enough, fast enough, to simply cut off the Crimea and deny the Black sea area to the Russians, and allow it to "whither on the vine", in the same way they did at Leningrad? Is this a good idea, bad idea, impossible, or possible? If a good or bad idea, why or why not?
Could Rommel in North Africa have done anything differently to help (even if that includes not being sent there in the first place)?

Could the Germans control the Black sea?

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The war against Russia will be such that it cannot be conducted in a knightly fashion. This struggle is one of ideologies and racial differences and will have to be conducted with unprecedented, unmerciful and unrelenting harshness. -Adolf Hitler

Well my question "what if" involves everything anyone thinks possible in the scenario described, including such things as "only if Turkey also came in the war on the axis side, then - ...?"

To control the Black Sea,the Germans had to control and capture the West coasts of the Caucasus and reach the frontier of Turkey;I don't think this was possible in 1941,due to the weather it was impossible already in september,and if they reached the Turkish frontier,they did not deed the help of Turkey .

Wasn't Moscow exactly the place Stalin feared Hitler would strike, and had be convinced out of that idea by his generals to deal with the Germans in Crimea? If memory serves, that's where the bulk of the Red Army reserves were until they came out to counter encircle Stalingrad.

Your what if is ambiguous, are we taling Barbarossa (1941) or Case Blue (1942) ?.
In 1941 the Germans made a half harted effort against Crimea then opted to go for Rostov, in 1942 clearing out the Crimea was necessary to avoid having to leave a large force to screen the forces there.
Supplies could flow through Kerch so the Crimea would not be isolated until much of the Caucasus was under German control. Also the Soviet navy was much stronger than anything the axis had in the Black Sea, and with Sebastopol in soviet hands the axis needed to garrison a very long coast against brigade size landings the Soviets were capable of doing (and did a few times).
Leaving an Army and a strong fortress unengaged in their rear would require a large screening force, looking at what happened at the Odessa siege, and later south of Stalingrad even the whole Rumanian Army may not be enough.

In 1941 clearing the Crimea instead of pushing to Rostov, that they were unable to hold, made more sense in hindsight, screening the Crimea is more or less what they did.
In 1942 screening the Crimea would probably not make the AGS spearheads stronger, Von Manstein's 11th Army was flagged for an attack on Leningrad anyway not an AGS reinforcment. A better 1941 what if would be Von Manstein and the siege experienced 11th at Stalingrad instead of Von Paulus and 6th Army.