Cook the pasta in boiling salted water according to the instructions on the packet. Clean and trim the mushrooms. Halve mushrooms, cut shiitake into slices. Cut oyster mushrooms smaller according to size.
Peel and chop the onion. Drain the tomatoes and collect the oil. Chop the tomatoes. Drain the pasta and let it drain. Heat 4-5 tablespoons of tomato oil in a large pan and fry the mushrooms.
Add the onion and tomatoes and fry for 1-2 minutes. Season with salt and pepper. Wash the thyme, dab dry and put aside some for garnishing. Finely chop the rest. Whisk eggs, milk and thyme, season with salt, pepper and nutmeg.
Place the pasta as nests in a greased casserole dish. Spread the mushroom mixture in the dish. Pour egg milk over it, sprinkle with cheese. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for 30-35 minutes.
Serve garnished with thyme. Tomato sauce tastes good with it.