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Pre-heat the oven to 180 degrees Celsius or 350 degrees Fahrenheit and coat the muffin tin with oil. Peel and finely grate the potatoes. Squeeze as much liquid from the grated potatoes as possible and add to a bowl.
Peel and finely chop the shallot and add it to the grated potatoes. Add an egg along with a handful of grated cheese. Season with pepper and salt and add a large tablespoon of flour.
Divide the potato mixture over 8 muffin tins and use your fingers to create a small bowl of potatoes.
Bake the rösti 'bowls' about 10 minutes in the pre-heated oven. Add a small egg in every rösti bowl and bake for another few minutes in the oven. The exact time depends on how you like your egg.
Use a spoon to transfer the muffins out of the tin, if you coated the tins with oil it should be easy. Season the eggs with some more pepper and salt and garnish with chives or parsley. Enjoy!