This is not something I came up with.
G1: Make sure you end your turn with a fighter on Tobruk, a tactical bomber on Southern Italy, and your planes on your german air base.
UK1: Taranto probably happens. (If it didn’t Italy is probably fine).
I1: Move everything that can go to Alexandria. Move your sub-saharans up next to Egypt. Make sure your planes are on your air base. Keep your one remaining transport alive. Buy a fighter or whatever you want, so long as it is in support of attacking Egypt in some way.
G2: Destroy whatever is left from Taranto with your air, land in Alexandria. If you took Southern France G1 (with 1/2x mech, 2x tank), you can potentially build a transport or two and move troops in to load up. This is not required, but helps a ton.
I2: Slam everything you can into Egypt. Retreat before you lose your planes (though risking losing just 1 is sometimes acceptable). Your fighters must land back in Africa. You will probably lose. Maybe not. Move everything else in africa close to Egypt (all 3 units). Have units in Greece to pick up if your transport off of Egypt lives. Buy another transport + whatever else you may need.
G3: Strafe Egypt with your planes. This will potentially hurt, but it’s an early victory city that keeps Italy in the game. If you build med transports, and were able to keep them alive, then you can take those as losses instead (but maybe keep 1 ground unit for the 5 IPC NO, this is probably worth the loss of a plane if Italy can keep Egypt). Do not strafe if there’s obviously no chance at victory, or if the victory means a loss of basically all of the luftwaffe.
I3: Slam Egypt again for the final time assuming all has gone well up to this point. You will probably win if you haven’t already.
UK has a good chance at stopping this if they send a lot of planes to Egypt, and/or if they build a factory there UK1, and/or if they had their transports ferrying from south africa. But you can stop them from doing a lot of that by keeping Britain scared with a Sea Lion feint from Germany.
UK must invest nearly everything they have into Egypt to keep it safe from this, and must be very clever with their boats.
UK can also retreat to Trans-Jordan, which makes the situation complicated.