The key to cooking cabbage is to cook it quickly.
If you can cook cabbage in 5 minutes or less, you will reduce and even avoid that cabbagey smell that can foul a kitchen.
Cabbage contains several sulfur-containing compounds which break down when cooked to release hydrogen sulfide, a gas which has an odor akin to the stink of rotten eggs.
The smell associated with overcooked cabbage doubles between the fifth and seventh minutes of cooking.
So cook cabbage in 5 minutes or less.
How to Cook Cabbage:
The smaller the cabbage is cut the less time it will require to cook.
Stir-fry. If you plan to stir-fry the cabbage, coarsely shred it. Heat the pan over high heat. When the pan is hot, add the oil and swirl it quickly to coat the pan. When the oil is hot, add the cabbage and stir briskly.
Sauté. You can sauté whole cabbage leaves in 2 to 5 minutes.
Boil. If you plan to boil the cabbage, slice it into thin wedges. Bring the water in your pan to a boil. When the water is boiling, add the cabbage wedges to the water. Cabbage wedges can be boiled in as little as ¾ inch (1.9 cm) of water.
If you want to boil a whole head of cabbage, boil the cabbage for 5 minutes, drain off the water and then cover the cabbage head with fresh boiling water and continue.
Steam. You can steam cabbage wedges in 10 to 20 minutes if you cut the head into quarters. To steam a full head of cabbage, you will need about 30 minutes.
Braise. Cabbage can be braised in a heavy-bottomed pan with butter and just a little water.
Don't over-cook. Cook it until it is just tender and no more. That way it will retain its crunchy texture and be mild and sweet to the taste.
Overcooked cabbage not only smells bad, it turns limp and pasty, and loses much of its nutrients.