Using the quantities of ingredients mentioned above, prepare the béchamel sauce.
Meanwhile, peel the potatoes, wash them, and slice them thinly. Wash the zucchini, trim them, and slice them into 3-5 mm (1/8 to 1/4 inch) rounds.
Butter the baking dish and sprinkle with breadcrumbs.
Layer the potatoes and sprinkle with a bit of salt. Cover the potatoes with a couple of tablespoons of béchamel.
Add a layer of zucchini, sprinkle with salt, and cover with béchamel.
Continue layering until all the ingredients are used up.
Bake in a preheated non-ventilated oven at 180°C/350°F for about an hour (160°C/320°F for 45-50 minutes in a ventilated one). Ten minutes before it's done, sprinkle the casserole with grated cheese.