Melt 2 tablespoons of the butter in a microwave safe bowl and set aside. Peel and grate the potatoes with the shredding attachment of a food processor, or on the wide holes of a box grater. Transfer potatoes to a bowl, and season with salt, pepper, and nutmeg. Drizzle the oil and melted butter over the potatoes and toss to coat evenly. Heat a medium non-stick skillet over medium heat. Add the potatoes and spread to evenly fill the skillet. Cook the potato cake, adding a few nut size bits of the remaining butter around the edges until the underside is crispy brown, about 10 minutes.
Reduce the heat to medium-low flip the cake sliding onto a plate and then inverting back into the pan. Cook; adding the last of the butter as before around the edges, until golden brown and potatoes are cooked through, about 10 minutes more. Serve immediately.
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