Peel and finely dice the shallots and garlic. Wash and finely dice the carrot and celery, or peel them if necessary. Clean the mushrooms and finely chop them in a food processor. Alternatively, finely dice them with a knife or slice them thinly.

Heat oil in a pan or pot, fry carrots, celery, garlic and shallots with a pinch of salt for about 2 to 3 minutes, until the shallots are translucent.

Add the ground meat, break it up with a wooden spoon, and brown it over medium-high heat for about 3 minutes without turning. Then stir and cook for another two to three minutes until evenly browned and crumbly. Add the tomato paste and sugar and cook for about 1 minute.

Now add the chopped mushrooms to the pan and sauté for two minutes. Then reduce the heat and deglaze first with the red wine and then with the strained tomatoes.

Tie the bay leaf, thyme, and rosemary into a bundle with kitchen twine, place it on top of the sauce, and simmer over low heat with the lid on for 30 to 60 minutes.

Preheat oven to 200°C. Turn off the stove, remove the herb bundle, add milk and season with salt, pepper, balsamic vinegar and oregano.

Slowly melt the butter in a saucepan. Add the flour and stir well until a roux forms. Gradually pour in the milk, stirring continuously until the sauce is smooth and lump-free.

Spread a little Bolognese sauce on the bottom of the baking dish. Arrange a layer of lasagna sheets side by side in the dish and carefully spread about half of the béchamel sauce over them. Spread about half of the Bolognese sauce on top and repeat the process once more, finishing with the grated cheese.

Bake the lasagna in the oven at 200°C for 35 to 40 minutes, then serve.