Preheat oven to 375°F (190°C).

Peel potato and grate with a fine box grater. Squeeze out as much of the juice as possible from the finely grated potato. Add a little salt and pepper.

Combine grated potato and shredded cheese. Divide into 4 equal portions.

Heat a large non-stick fry pan. Spread out each portion of grated potato and cheese mixture like a pancake of about 3½ inch diameter in the pan. Cook for 1 to 2 minutes. Gently flip over. This may be a little tricky as the mixture is very soft. Gently pat and reshape with spatula if they clump up. Cook for another 1 to 2 minutes or until lightly browned. Remove and place on a plate. Allow them to cool slightly.

Press each of the shredded cheese and potato pancakes into 4 indentations of an ungreased and unlined non-stick muffin pan to form a cup. Crack an egg into each cup. Add a little salt and pepper to each egg.

Bake for 15 to 18 minutes depending on how cooked you like your eggs to be.

Remove and serve immediately with bread or toast.