Sauté the onion, garlic, carrots, celery and mushrooms in the oil.
Remove the stem from the tomatoes, puree and pour in. Season with thyme, tomato paste, salt and pepper and reduce a little.
For the bechamel sauce, melt the remaining butter, add the flour and pour in the milk while stirring. Season with nutmeg, salt and pepper and simmer for approx. 10 minutes.
Preheat the oven to 180 °. Grease a lasagne dish. Layer the pasta, vegetable sauce, bechamel, mozzarella and ¾ of the parmesan alternately in the pan. Finish with bechamel, parmesan and flakes of butter. Bake for about 45 minutes.