Olive Oil Fried Potatoes with Over Easy Eggs (Huevos Estrellados)

The potatoes in this comforting Spanish dish should not be brown and crispy like French fries; they should be limp, creamy, and soft with only a slight crispness at the exterior. To achieve this, add the potatoes to the oil all at once to temporarily drop the frying temperature, essentially poaching the slices until the oil gets back up to frying heat.