Cover the potatoes and boil them in water for about 20 minutes. Drain, quench, peel and let cool down a little.
In the meantime clean, wash and quarter the cabbage and cut it into fine strips from the stalk. Heat the oil in a large pan. Fry the gyros in it for 2-3 minutes, turning them over. Take them out. Sauté the cabbage in the frying fat for about 10 minutes.
Season with salt and pepper. Add cream, bring to the boil and simmer for about 3 minutes. Season to taste with salt and pepper.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Cut the potatoes into slices and spread them in a large greased casserole dish. Mix gyros and cabbage and spread on the potatoes.
Wash the thyme, dab dry and remove the leaves. Season crème fraîche with salt and pepper and spread it on the casserole. Grate the cheese directly on top. Sprinkle with thyme. Bake in a hot oven for about 30 minutes.