Pour the oil to a depth of about 1½ inches into a heavy frying pan large enough to hold at least 5 eggs at a time. Heat the oil until the surface ripples gently (175°F on a frying thermometer).
Be careful not to overheat the oil as this will make the whites puff and brown. They should remain smooth, almost like an egg poached in water. Break the eggs into saucers and slide into the fryi