Cut 2/3 of the leek from the green side, clean and wash. Cut about 4 cm of the green into thin strips. Halve the leeks crosswise. Peel and wash the carrots. Cook the carrots in boiling salted water for about 4 minutes.
Add the leek after about 2 minutes. Remove the vegetables and dab them dry a little. Heat the oil in a pan. Fry the leek and carrots in portions all around and season with salt and pepper. Take them out and put them in an ovenproof dish.
Heat butter in a pan and fry the spaetzle in it for 2-3 minutes until golden brown. Mix the spaetzle with salt, pepper and nutmeg. Grate cheese. Mix half of the cheese and the spaetzle and put it on the vegetables.
Sprinkle with remaining cheese. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for 15-20 minutes. Sprinkle with leek strips.