Boil two cups of water in a wok or frying pan. Dump in the trimmed beans and cook for two to three minutes. Scoop out and drain.
Discard the water and wipe the wok or drying pan dry. Set the stove to medium heat. Reheat the wok and frying pan.
Pour in the sesame seed oil.
Saute the chopped garlic and drained green beans for about half a minute or just until the aroma of garlic starts to waft through the kitchen.
Pour in the mirin (or whatever rice wine you're using) and soy sauce. Stir.
Cook the green beans, uncovered, for another two to three minutes or until done and until they have soaked up much of the sauce.
Transfer the cooked beans on a plate. Spoon the garlic and whatever sauce is left over them.
Sprinkle in the sesame seeds and serve at once.