Cook the potato in boiling salted water, drain them and mash with a fork. Add the parsley and season with olive oil, salt and pepper. Arrange the mashed potatoes at the bottom of a gratin dish. Set aside
Slice in eggplant vertically (0.7-1 inch thick). Heat some olive oil in a pan and fry the eggplant for a few minutes on each side. Season lightly and set aside
For the Béchamel: in a saucepan, melt the butter on medium heat. Add the flour and whisk thoroughly. Pour in the milk, whisking constantly until the béchamel thickens. Season with salt, pepper and nutmeg.
Slice the cheese. Preheat oven to 325-50 F
Place several slices of eggplant on top of the mashed potatoes. Add a layer of béchamel a couple of slices of cheese, then the rest of eggplants. Finish with some béchamel and slices of cheese