I am sure there are east front experts who could find many problems with this. But I thought I would give it a try for fun:
1) General Wever lives, Germans keep Ju88 a fast rangey level bomber, increased levels of pilot training, better organization and lower levels of losses in Battle of Britain make a Luftwaffe with a larger level bomber force that can reach further without having to rebase.
2) With the extra air power Guderian closes the ring sooner and keeps them closed in Smolensk and Byransk encirclements.
3) German abort Leningrad offensive earlier and avoid getting drawn to Kursk and Kalinin, focus on getting around Moscow
4) Germans manage to get weak mobile forces across the roads and railways leading to Moscow (i.e. on the east side of Moscow).
5) Russian command and control is chaotic and weak, Zhukov has a hard time getting around to everyone. Instead of overwhelming the Germans holding the ring, most Russian forces, a lot of which are militia, just exfiltrate the weak ring and get out, joining the good Siberian forces already on the outside.
6) Germans more closely ring the city still held by police, remaining militia, but their is little Soviet command and control, Germans mange to break in at a number of places and grab some key land marks and manage finally to capture some supplies intact, especially at Vnukovo airport and such military bases.
7) Soviets still hold most of the city, its just too big to really take, population just starves, a trickle tries to escape, Germans are content with this status, trying to secure just the main communication routes through the city, not messing with the rest.
8) Soviet counteroffensive is delayed by the loss of the use of the Moscow communication center, still lots of railways leading to battle front, but lateral movement difficult. Counter offensive starts December 27th.
9) Germans use extra the time to try push railroads further east and repair airfields around Moscow and get their mobile units a little further back since their kind of useless in the extreme cold. Deserately cold Germans start looting Moscow residents of Winter clothing. No purges of Bock, Guderian etc occur yet.
10) Soviet counter offensive bigger than OTL with the extra time to prepare, and a more concentrated effort.... Bock, Guderian and others issue retreat orders, Hitlers outraged, sacks them January 2nd.
11) Germans start flying in supplies to Vnukovo airport just west of Moscow which becomes a fortress with a big enough ring to allow Stalingrad style airlift which works in the Winter of 41 -42 (General Wever helps organize). Kluge is in charge inside the ring. Model is also in the ring and becomes a fireman of sorts.
12) Germans try to keep somewhat clear and repaired the Moscow - Minsk paved highway as a retreat and supply road, fortresses are established in the cities along the road, Luftwaffe tries to fly top cover over the road as best as it can.
13) Soviets do better than OTL initally, but later have supply issues due to loss of Moscow and lack of good intact communication routes but do take major chunks of territory back.
13) Germans in early April 1942 open a thin supply line with a thin long salient all the way to the Vnukovo airport to the west of Moscow, but Moscow is liberated by the Soviets (and in the city is in shambles).