Slice the onion as thinly as possible. (A large shallot can be substituted for the onion.) Fill a large, non-stick sauté pan with oil to a depth of 6 mm (1/2") deep and place the pan over medium heat. The oil should be at about 160 °C (325 °F).
Separate the onion slices into individual layers and dust with a small amount of flour. Shake off any excess.
Fry the onions briefly, in small, batches, until they start to color.
Drain well on absorbent paper and set aside. The onions can be made a few minutes in advance and kept warm in a 75 °C (170 °F, thermostat 2-3) oven. Leave the oven door slightly ajar so that moisture doesnt accumulate. Moisture causes the fried onions to lose their crispness.