Peel the potatoes and slice them very thin, preferably with the help of a mandolin or the slicing blade of a food processor.
If you don't plan to use the potatoes immediately, immerse them in water as you go. And when you'r ready to cook, drain and pat the potatoes slices dry.
Grease a baking dish with olive oil. Cover the bottom with the potatoes in a single layer of slightly overlapping slices like the shingles of roof. Drizzle with olive oil and sprinkle generously with salt.
Lay down a second layer of potatoes in the same way.
Prepare the batter by whisking together the flour and milk until perfectly smooth, then season with a good pinch of salt and, if you like, a few leaves of fresh marjoram and/or a scrape of nutmeg. The batter should be perfectly smooth and quick thick, though just barely pourable.
Scrape the batter over the potatoes, then use a spatula to level it out, making sure to cover all the potato slices.
Top with the grated cheese(s) and drizzle generously with olive oil.
Bake the potatoes in a hot (200C/400F) oven until cooked through and golden brown on top, about 20-30 minutes.
Serve warm or at room temperature.