There were several purposes to Operation Torch.
1) Get the US into the war. FDR wanted Americans fighting the Axis, especially before the November 1942 elections.
2) Push the Axis off of Africa so that the Mediterranean Sea convoy routes are more secure.
3) Get France into the war by liberating French North Africa to open up French manpower reserves. This was not very realistic, but was a real aim. When Torch was planned, Germany had achieved early success in Case Blue and there was concern that the Soviet Union might get knocked out of the war or make a separate peace. The Americans wanted additional manpower if the British and them were going to have to defeat Germany without the Soviets.
In this scenario, the British probably control the sea routes in the Mediterranean. If Libya fell in 1940 or early 1941, it is even possible that they might even have Sardinia or Sicily themselves.
So what do the Allies need to do ITL? The US needs to fight somewhere. Since invading France is just as infeasible, this leaves either Norway or a Meditteranean operation. Norway would be bad idea, so it has to be the Med.
Securing the Mediterranean Sea is not as crucial ITL as in ours, but there are lots of possible objectives. If Sardinia or Sicily are not already occupied, they are potential targets. Crete is too far east for an initial landing by the Americans. There is still French North Africa.
But do they need French North Africa? Not for further operations - the British have already secured the Med. The US could sail to British Libya is needed. There is still the chimera or opening up a large body of French troops. After some thought, I suspect that is too much of a target in 1942.
The major changes I see are:
1) facing no siginficant opposition, the US can plan a landing in Tunisia as well as Morocco and Algeria. This will secure all of Africa much, much quicker.
2) The Axis will not land any troops into Tunisia. It's already clearly lost.
3) The invasion of French North Africa must be a prelude to US troops fighting the Axis - not French - troops. So Torch will happen sooner - perhaps in August or September, with the hope that a subsequent invasion of an Axis held island can be done before November. Depending on whether you think the British had already occupied any of the islands, we will see Americans land on Sicily, Sardinia, and Corsica.
Allied planning was very contingency based at this time. The US put a cross channel invasion at the top, while the British preferred a flanking strategy. What would get pushed always depended on what was actually feasible at the time. The original plans for Torch assumed a quick victory that would free up troops for a 1943 invasion of France. Delays in Tunisia destroyed that option so the US agreed to British proposals for a landing in Sicily and later Italy.
In this scenario, a quick overrun of French North Africa and Med islands means a 1943 invasion of France is at least a possibility. There are still very good reasons not to do that. I'm assuming the British win the argument again.
In which case, an invasion of Italy will happen ASAP in 1943. Assuming Italy wants out of the war, it all comes down to how quickly the Allies can land troops in Italy and where. Air bases in Sardinia can cover landing forces much farther north than Salerno. Will the Allies land troops north of Rome? If they believe Italy will quickly fold, then an aggressive commander could cut off all Axis troops south of Rome (perhaps south of Leghorn).
The US commander will either be Fredendall or Patton. The British commander may be O'Connor. Hopefully, Ike will pick Patton to lead any initial landings.
If so, British and US troops can cut off Italy very quickly. The Italian government surrenders. Rome falls quickly to Allied hands, and any Germans south of Rome are cut off. The Allies begin to slowly take all of southern Italy while 2 Allied armies advance north. The Germans probably advance into northern Italy holding the alps and possibly stopping the Allies near the Po River. There is probably at least one battle where the Americans are badly mauled on the Padanian Plain. If Patton is commanding, the damage can probably be contained. If Fredendall commands, it might be a true disaster. Most likely, 1943 ends with most of Italy in Allied hands, but the Germans having a good defensive position. However, the Allies threaten both southern France and the Balkans.
At that point, I suspect that Anvil happens right before or at the same time as the Normandy landings to speed up the liberation of France. In Italy, it's to push into the Veneto and towards the Ljublana Gap. Objective is to cut off German troops in the Balkans, link up with the Soviets on the Pannonian Basin, and get Romania and Bulgaria to defect.
If everything goes well, the war is over by Christmas 1944. This assumes a lot of Allied breaks, but it's not unrealistic. A few blunders or screwups, and not much changes from our timeline.