1. Peel the potatoes and cut into thin chips or not-too-thin slices; rinse in cold water and dry thoroughly.
2. Heat the olive oil in a deep frying pan to medium-hot (about 150 °C) and fry the potatoes for 10-12 minutes until tender, then turn up the heat and fry for 2-3 more minutes until golden and crisp.
3. Drain on kitchen paper, salt and pile onto a large platter; lay the ham slices over the hot potatoes so their fat melts slightly.
4. Pour 4-5 tablespoons of the oil into a smaller pan and fry the eggs one at a time: the edges should be crisp and lacy and the yolks runny.
5. Slide the fried eggs onto the potatoes and ham.
6. At the table, "break" the eggs with a fork so the runny yolk coats the potatoes – that's where the name comes from.
Tip: Baste the eggs as they fry: spoon hot oil over the whites so they set quickly while the yolks stay runny.
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