Grease a 9 x13" casserole dish. Add half of the parmesan cheese to the bottom of the dish.
Microwave the potatoes until soft,. Then slice and lay on top of the cheese in the dish. Sprinkle with ¼ teaspoon of Kosher salt.
Preheat the oven to 350℉.
Heat the oil in a skillet. Sauté the onion slices with ¼ teaspoon salt until softened and caramelized, stirring often. Remove from the heat. Top the potatoes with the caramelized onions. Sprinkle half of the cheddar over.
Whisk together in a large bowl the cream, milk. eggs, ⅜ teaspoon salt, pepper, cayenne pepper, nutmeg, minced parsley, and thyme leaves.
Add the egg/ cream/spice mixture and prosciutto, if desired. Top with remaining cheeses.
Bake 45-50 minutes or until a knife come out clean. Let sit 10 minutes. Slice and top with more minced parsley, if desired.