Heat the oil in a pan. Fry the turkey filets in it for 9-11 minutes on each side. In the meantime, carve 6 tomatoes crosswise. Add boiling water, rinse with cold water and remove the skin.
Quarter the tomatoes, cut out the core. Roughly dice the flesh. Peel garlic and onion. Finely dice onion. Press garlic through a garlic press. Remove turkey filets from the frying fat and put aside.
Sauté onion and garlic in the frying fat until transparent. Add the tomato paste and diced tomatoes, sauté briefly. Deglaze with stock and milk, bring to the boil and simmer for 5 minutes. Season with salt, pepper and sugar.
Stir starch with a little water until smooth. Stir into the tomato sauce and bring to the boil. Cut meat into larger pieces. Clean the savoy cabbage and carefully remove the leaves. Blanch in boiling salted water for about 2 minutes, rinse cold and drain.
Grease the bottom of an ovenproof casserole dish (approx. 30 cm long) and line it with 3 lasagne sheets. Spread a layer of cabbage evenly on top. Pour 1/3 of the sauce over it. Cover with 3 lasagne sheets.
Spread the meat on top and pour 1/3 of the sauce over it. Place 3 lasagne sheets on top. Add the rest of the savoy cabbage and pour the rest of the sauce over it. Wash and slice 1 tomato and place it on the sauce.
Grate the cheese, spread evenly on the lasagne. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for 35-40 minutes. Cut lasagne into pieces and garnish with salad.