Finely chop the onion, garlic, carrot and celery and fry gently together for about 15 minutes. Chop everything else into similar-sized chunks - not too big or it will take longer to cook. Add the squash and cook for another 10 minutes. Add the courgette and aubergine and cook for another 5 minutes. Add the chopped tomatoes and the mushrooms. Stir everything round and season with salt and pepper. Cook for another 20 to 30 minutes, or until everything is more or less cooked.
Meanwhile, melt the butter, then take it off the heat and stir in the flour. Return to the heat and add the milk gradually until you have a glossy sauce.
Layer lasagne - vegetables - white sauce - lasagne - white sauce - vegetables - white sauce - lasagne - white sauce - grated cheddar and parmesan. Bake in the oven at 200 degrees for around 30 minutes.