Prepare the Aubergine (Eggplant)
Wash the aubergine and cut into 1cm (just under half an inch) slices. Line a baking sheet with absorbent kitchen paper and sprinkle a thin layer of salt on it. Arrange the aubergine slices in a single layer and sprinkle more salt on the top. Set aside for at least 30 minutes while the salt extracts moisture from the aubergine.
Make the Tomato and Mushroom Sauce
Empty the can of tomatoes into a large saucepan and mash them down into small pieces. Add the basil leaves, torn up, and half a teaspoon of ground black pepper. Bring to the boil, then turn down to a simmer.
Wash the mushrooms thoroughly and chop into very small pieces, so they have a granular appearance. Peel the onion and chop into small pieces. Heat some vegetable oil in a frying pan (just above medium heat), add the onion and cook for about 5 minutes until softened but not browned. Halfway through the cooking, add the minced garlic clove.
Add the onion and garlic to the saucepan, turn up the heat under the frying pan to maximum, and quickly fry off the mushrooms, stirring constantly. The aim is to get rid of most of the moisture in the mushrooms. Add them to the sauce, stir well and simmer for 10 - 20 minutes.
Make the White Sauce (Béchamel)
Melt the butter in a small saucepan on medium heat. Sift in the flour a bit at a time and stir rapidly to incorporate it into the butter. When it has formed a smooth paste, add the milk and stir to incorporate. Add the mustard, if using. After a few minutes, the sauce should begin to thicken. Stir in some of the cheese.
Check both sauces for seasoning, remove from heat and let them cool down for 15-20 minutes.
Assemble the Vegetarian Lasagna
Preheat your oven to 230°C (445°F). If you are going to need to cut any of your lasagna sheets, soak them for a minute or two in boiling water so they don't shatter when you cut them. Grease your baking dish with butter. Rinse the salt and liquid off the aubergine slices.
Spread a thin layer of tomato sauce in the baking dish. Arrange aubergine slices in a single layer, and then add a layer of pasta, making sure the sheets don't overlap. Spread a thicker layer of tomato sauce onto the pasta, another layer of aubergines and another layer of pasta. Repeat the layering once more, then spread the white sauce on top. Sprinkle with the remaining cheese and bake for 20-30 minutes.
Serve the Lasagna
Once the lasagna is out of the oven, you must leave it for at least 20 minutes to let the sauces set a bit. Now you can slice it into squares and serve with salad.