Make the béchamel
Heat the butter in a heavy saucepan over moderately low heat until it has melted, then add the flour and cook the roux over low heat, with whisking, for 3 minutes. Add the milk in a fast stream while whisking vigorously to avoid lumps. Bring to a boil, then reduce the heat and simmer, whisking occasionally, 6-7 minutes. Season with salt and
pepper. Add all the grated Parmesan minus about 3 spoonfuls (set this aside for sprinkling on top of the assembled lasagna dish). Stir in the grated nutmeg.
Make My Mother's Tomato Sauce
Assemble the lasagne
If desired, you may precook the lasagne noodles. Working in batches, plunge 3-4 noodles at a time in a large pot of boiling salted water. Add one spoonful of olive oil to the water to prevent the noodles from sticking to each other. Do not cook the noodles through, but just until a bit soft, about 2-3 min, then drain them, pat dry and place them in one layer on a kitchen towel.
Spread a few spoonfuls of béchamel sauce on the bottom of a baking dish. Arrange some lasagne noodles over the sauce, without overlapping them (allow room for swelling during cooking), until the bottom of the dish is covered. Spread some spoonfuls of béchamel and tomato sauce over the noodles, then cover with another layer of noodles. Repeat the layering of sauce and noodles 4 to 6 times, depending on the serving size and the shape of the baking dish. Top the lasagna with the reserved Parmesan.
Preheat the oven to 205ºC/400ºF. Bake the lasagna, uncovered, until the top is golden-brown and the sauce is bubbling, about 30-35 min (or a 20-25 min if the noodles have been precooked). Let stand 5 to 10 minutes at room temperature before cutting and serving.