Slice potato into 1/8" thick slices and cut them into thin matchsticks. Rinse potato with cold water and drain, set aside.
Heat oil in a skillet over medium heat, saute garlic for 10 seconds. Add the potato, sprinkle two pinches of salt over and stir. Cover the skillet with a lid and reduce the heat to med-low. Cook for 1-2 minutes.
Open the lid and add the green beans, sprinkle with more salt and stir. Cover with the lid again and cook for another 1-2 minutes. Remove the lid and gently toss the potato and green beans until they are soft with a little body. You might need to adjust the time and heat to achieve the desired texture.
Season with more salt, if you need, and pepper. Sprinkle sesame seeds and gently toss together. Serve warm or at room temperature.