Clean the mushrooms dry or with damp kitchen paper and cut them into pieces. Fry them well in a pan with a little oil and the peeled garlic clove. Do not salt the mushrooms, otherwise they may release water and become rubbery. Add the chopped parsley to the mushrooms. Remove the pan from the heat.
Melt the butter for the bechamel sauce. Grate a little nutmeg. Add the flour and sweat it briefly while stirring. The flour must not turn brown. Mix the milk and water and add slowly, stirring vigorously. Bring the bechamel sauce to a boil once and then cook at a low temperature until it thickens well. Season with salt and nutmeg if necessary. The total cooking time for the bechamel sauce is about 15 minutes.
Preheat the oven to 180°C with top and bottom heat. Put the water in a larger pot, salt it. Once it boils, cook 4-6 lasagna sheets each briefly (1-2 minutes). Take out and put on the next sheets.
In the meantime, prepare a layer of lasagna: Cover the bottom of the baking dish with the briefly cooked pasta sheets. On top, add a layer of mushrooms, then the bechamel sauce and the grated cheese. Season well with pepper. Repeat the layers until all the ingredients are used up. The top layer: béchamel sauce sprinkled with plenty of cheese.
Bake in hot oven for about 40 minutes. If the lasagna darkens too quickly, cover with aluminum foil. The lasagna is ready when it has turned a nice golden color.
Notes
If you don't want to pre-cook the lasagna sheets dry, pay attention to the consistency of the bechamel sauce. In this case, the sauce should be a little more liquid. This will prevent the pasta from cooking through. If you buy fresh lasagna sheets, it is easier and also saves the short pre-cooking time.