Heat the oil in a saucepan and fry the chopped onion until translucent. Add the ham cubes and fry for a few minutes. Clean the savoy cabbage, cut it into small pieces and put it in the pot. Steam with the lid closed for about 10 minutes, adding a little water if necessary.
Chop the dried and fresh tomatoes and stir into the savoy cabbage. Put the lid back on the pot and let the vegetables cook through. Finally, stir in the balsamic vinegar, the turnip tops and the pesto and season the dish with salt and pepper to taste.
It tastes best when the dish can sit through for a while. The dish is very low in fat and is enough for two people as a main course and for 4 people as a side dish, for example with hot sausages.