Remove the ends and skins from the potatoes. Cut into thin slices about 4 mm thick.
Fill a large pot with hot water, add salt as you would for pasta, bring to a boil, and add the potatoes. Once the water returns to a boil, cook the potatoes for 3 minutes. They should be cooked but still crisp.
Using a slotted spoon, transfer the potatoes to a baking dish.
While the potatoes cool, spread the béchamel on the bottom of the baking dish.
Preheat the oven to 190 degrees Celsius (375°F).
Mix the breadcrumbs, cheese, oregano, and salt, and pour the mixture into a large baking dish.
Coat the potatoes in the mix, shake off any excess breadcrumbs from the slices, and arrange them vertically in two rows until the baking dish is full. If there are any breadcrumbs left over, sprinkle them over the potatoes. Sprinkle with more Parmesan and drizzle with oil.
Bake in the oven for 15 minutes, then turn on the grill function for the remaining time I have indicated, or until they are golden brown to your liking. If you don't have a grill, increase the oven temperature