This is the original recipe for Delmonico Potatoes, a popular dish served for decades at New York City's famed Delmonico's Restaurant. Internet hoaxes occasionally circulate claiming to be the original recipe from Delmonico Hotel (made with potatoes, rice, butter, flour, milk cheddar cheese, salt, pepper). But the original recipe was created in 1838 by an unknown chef at Delmonico Restaurant (a separate business in a completely different part of NYC). The original title translated to 'fricasseed potatoes'. Only more recently has it become more commonly referred to as 'Delmonico Potatoes'.
Wash (but do not peel) the potatoes, and quarter them lengthwise (so that, after cooking, they can be grated or sliced into the longest shreds possible). Bring 8 cups of water to a boil and then add the potatoes. Let boil for 10 minutes so that the potatoes are not cooked through. Immediately submerse the hot potatoes into cold water, and let them cool for at least 30 minutes. Grate or slice the potatoes into long strips.
Mix together in a bowl the other milk, cream, salt, pepper, parsley, and nutmeg.
Preheat a large frying pan over medium heat and then add the potatoes and liquid mixture. Fold them together well but gently, without mashing the potatoes, and cook for 10 minutes, mixing lightly occasionally so that they do not burn. Remove from the stove and fold in 1 tablespoon of the cheese.
Transfer the potatoes into a pre-buttered baking dish and arrange evenly. On top, sprinkle the remaining 1 tablespoon of cheese.
Preheat the over to 425°F.
Place the uncovered baking dish into the upper-third of the oven, and bake for 6 minutes or until lightly browned. Sprinkle the sliced green onions on top, and serve immediately, while still hot.