Cut the cheese into small cubes.
Peel and dice the onions. Rinse, trim and halve the bell pepper, remove the seeds and ribs and cut into strips. Wipe and trim the mushrooms and cut into slices.
Sauté the onion, bell pepper, peas and mushrooms in some butter in an ovenproof, deep pan and season with salt and pepper.
Beat the eggs with milk and season with salt, pepper, cayenne pepper, savory and nutmeg. Mix with the cheese and pour into the pan. Mix well and distribute everything evenly. Cook for half a minute on the stove and then transfer to the oven for about 20 minutes at 180°C (approximately 350ºF).
Cook the spaetzle according to package directions.
To serve, tip the omelet out of the pan and onto a plate. Cut into pieces and serve hot with the noodles.