Peel and chop the onions. Heat the oil in a casserole dish, fry the onions in it until transparent, dust with paprika and add sauerkraut and oregano. Pluck the sauerkraut apart. Braise for about 5 minutes while turning.
Then deglaze with broth and braise at medium heat for about 15 minutes. Then season to taste with salt, pepper and sugar. In the meantime mix cream, sour cream and Gouda. Put the gyros in a hot pan without fat and fry them while turning for about 10 minutes.
Place the braised sauerkraut in an ovenproof dish (approx. 30 cm long). Spread the gyros evenly on top. Pour cream and cheese evenly over it. Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for approx. 25 minutes.
Remove from the oven and serve garnished with oregano to taste.