Peel and finely chop the onion. Heat the oil in a pot. Fry onion and rice briefly. Add 375 ml broth and tomatoes, cook for about 20 minutes. Stir from time to time.
Season to taste with salt, pepper and marjoram. Clean and slice the mushrooms. Heat the fat and fry the mushrooms in it. Dust with flour and deglaze with 250 ml broth and milk. Stir in half of the cheese.
Season to taste with salt and pepper. Clean the cabbage and remove 12 large leaves, cut out the middle rib (use the rest of the cabbage for other purposes.) Blanch the cabbage leaves briefly in boiling water. Remove the leaves and let them drain.
Spread the rice on the cabbage leaves. Roll up the leaves. Put the rolls in an ovenproof dish, pour sauce over them and sprinkle with the rest of the cheese. Bake in a preheated oven (electric oven: 200 °C/ convection oven: 175 °C/ gas mark 3) for about 10 minutes.
Serve gratinated Chinese cabbage rolls garnished with marjoram.