Bring a small pot of salted water with a bit of vinegar up to a boil. In a large sauté pan, heat the olive oil. Season the grated potatoes with salt and pepper. Divide the potatoes in half. With one half of the mixture, make four small mounds of grated potatoes. Using you hand, gently press the potatoes down to 1 inch thick. Lay 1/4 cup of the duck confit on top of each potato mound. Spoon about 2 tablespoons of the onions on top of the confit. Cover the top of the cake with the remaining potatoes. Gently press the cakes down to secure the cakes. Using a metal spatula gently place the cakes in the hot oil. Fry the cakes for 2-3 minutes on each side or until golden brown. Remove the cakes from the oil and drain on a paper-lined plate. Season the cakes with salt and pepper. Crack each each into a small cup. When the water is up to a boil. Gently pour the egg into the water. Cook the eggs for about 2 to 2 1/2 minutes. Remove the eggs with a slotted spoon and drain on a paper-lined plate.
Yields: 4 cakes