Finely chop, grate or process onion, garlic and carrots.
On a medium heat warm up the 2 tbsp olive oil in a big frying pan, add the vegetables and fry stirring occasionally for 5 minutes.
Finely chop the mushrooms (you can also process them but be careful not to over-process them) and add to the vegetables, fry for 5-7 minutes until the liquid evaporates.
Add the canned tomatoes, red wine, bay leaf, sugar and a bit of salt and pepper, stir and on a medium heat cook for 40 minutes, stirring from time to time, till the sauce thickens. When the sauce is ready, check the taste and adjust seasoning if necessary.
In the meantime prepare the béchamel: in a heavy-based pot warm up the olive oil, add the flour and stir it quickly and very well. Pour the milk (cold), vigorously whisk it and bring it to a simmer on a low heat, season well (salt, pepper and nutmeg). Constantly stir the sauce till it boils and thickens. Add the Parmesan cheese, check the seasoning again, adjust if necessary.
Pre-cook the lasagna sheets (if they require pre-cooking): use a big pot and cook only 2-3 sheets at a time so they don’t stick together. If you don’t use them straight away, once cooked put them on plates making sure they don’t touch each other to prevent them from sticking together.
Preheat an oven to 180 Celsius degrees.
Put a quarter of béchamel sauce on the bottom of a square or rectangular oven proof dish*, cover it completely with lasagna sheets. If necessary trim them so they match the size and shape of the dish.
Spread half of the mushroom sauce over the lasagna sheets, then spread the second quarter of the béchamel and cover with some more lasagna sheets; repeat one more time.
Cover the top layer of lasagna sheets with the rest of the béchamel and sprinkle with grated parmesan, put to the hot oven and bake for 30 minutes.
* I used 22 cm x 30 cm dish and for this amount of ingredients, I wouldn’t recommend using a bigger one as the lasagna would be too thin.