Bring a large pot of salted water to a boil. Add the spaghetti and cook it until al dente. Drain it, retaining some of the cooking water and place it in a large serving bowl. Lightly coat with olive oil.
While the pasta is cooking, heat 1/4 cup of olive oil in a large skillet and fry the eggs sunny side up. Add salt and pepper to taste. When the eggs are almost done, add the cheese to the pasta and a bit of the retained cooking water. Mix thoroughly.
Divide the pasta into equal portions on the serving plates, and top each with an egg. Serve immediately.