1. In a frying pan heat the oil and butter. Cook the potatoes turning them once, 15-20 minutes. Add onions and cheese. Season to taste. Continue cooking 10-15 minutes, turning the potatoes once or twice. Potatoes and onions must be tender and brown. Set aside in warm individual plates.
2. Mix the remaining butter with the oregano to form a paste.
3. Put one egg over the potatoes in each individual plate and dot with oregano butter.