Bring a pot of water to a boil; cook beans in boiling water until bright green, about 2 minutes. Immediately transfer green beans to a bowl of ice water to stop the cooking process. Drain and dry beans with paper towels.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Pour flour into a bowl. Whisk egg in a separate bowl. Pour bread crumbs into a third bowl.
Coat green beans with flour; transfer to beaten egg and coat evenly. Press coated green beans into bread crumbs.
Fry breaded green beans, working in batches, in the hot oil until golden brown, 3 to 5 minutes. Transfer fried beans to a paper towel-lined plate to drain.