In a large pot add water and 1 teaspoon salt to cook the pasta. Bring water to a boil and cook pasta according to package directions.
When the pasta is cooked, drain and toss with the mizithra and oregano. Transfer to serving dishes and set aside until you fry the eggs.
Heat the olive oil in a medium size skillet over medium heat; the oil should be 1 cm deep in the pan. If you are not using a non-stick surface, spray your pan with cooking spray before adding the olive oil.
Crack your eggs into a bowl one at a time and gently slip them into the hot oil. The eggs should start to cook immediately, with the egg whites turning opaque very quickly.
Turn the heat down to medium and cook eggs carefully. Tilt your pan to one side occasionally to pool the hot oil into one side of the pan. This will help stop any oil splattering. Also, with a tablespoon, scoop up some of the hot oil and carefully pour it over the egg yolks. Repeat this several times, depending upon how runny (or not) you want your yolks. For this dish, a runny yolk is preferable. Watch video here.
Continue to cook your eggs until you have a nice, golden, crispy outer edge to your egg whites.
Using a slotted spatula, carefully remove your eggs from the frying pan and transfer one egg to each dish of pasta. Pour the olive oil which is in the pan over the pasta as well, dividing it as evenly as possible.
Season with salt and pepper and additional mizithra if desired.
Break the yolk over the pasta and enjoy!