Cut the leek lengthwise and cut into narrow stripes. Cook the spaghetti al dente in salted water, add the leek stripes for the last three minutes. Remove the cooking water, cool with cold water and drain.
Preheat the oven to 200°C.
Peel the carrots off, cut into ca. 5mm small cubes. Cut the button mushrooms into four. Heat the oil and roast the mushrooms. Add carrots, salt and pepper, let cook for about 5 minutes. Coarsely chop the pepper and mix with the vegetable.
Give form to spaghetti and leek nests with a meat fork and align them on a gratin platter. Spread the vegetable mix on the nests. Mix milk, egg and Gruyère AOP, add salt and pepper. Pour onto the nests. Grill 25 to 30 minutes in the oven.