Remove the outer leaves from the purple cabbage and wash it. Cut it in half lengthwise. Work with one half first. Turn it over on the cutting board so that the cut side is facing the board. Cut out the core in a wedge shape. The core is slightly bitter and does not taste good. Slice the remaining cabbage. Do the same with the other half.
Place the chopped cabbage strips in a large pot that can hold them all. Pour olive oil over them and sprinkle with salt. Mix together. Cover and steam the cabbage over medium heat, stirring occasionally. It is important not to add water, as this will make it too soggy. It will release its own juices. Towards the end, I usually add diced apples so that they don't cook completely.
I don't like to cook cabbage until it's too soft; I prefer it when there's something to bite into. Usually, after simmering for 30 minutes, it reaches the right consistency.
At the end, I usually stir in a tablespoon of honey.