Wash beans and pat dry. Cut the ends and chop lengthwise (french style). Boil salted water in a pot. Add the beans and cook for 3 minutes, or al dente. Drain and place in a bowl with ice water to set the colour and stop the cooking. Leave 5 minutes and drain.
In a bowl, place cooked beans, flour, eggs, cheese, and green onions with salt and pepper. Stir with a fork or hands until well blended. (Or replace flour, eggs, cheese with the eggless batter.)
Heat a large fry pan over high heat. If you throw water droplets, they should dance and evaporate almost immediately. Reduce heat to medium. Add one tablespoon olive oil, and place a generous scoop of green bean mixture in the pan, forming patties and cook for 5 minutes. Turn and cook 5 minutes more.
Remove to a plate lined with a tea towel and continue with the rest of the mixture. Serve hot or at room temperature, sprinkled with salt.