Scrub the potato and cut into 1-inch cubes. Trim the green beans then cut in half and rinse under cold water.
Boil a pot of water and 1/2 tsp salt over high heat. When water begins to boil add the potatoes and cook until just slightly tender, about 7 minutes. Drain the potatoes.
Heat the oil in a large non-stick skillet over medium-high heat. Add the potatoes to the pan and cook, without stirring, until the potatoes begin to brown, about 7 minutes.
Add the green beans to the pan along with the garlic powder, 1/4 tsp salt, and 1/4 tsp pepper and stir to combine with the potatoes. Cover the pan and cook 5 minutes or until beans are just slightly tender. Add salt and pepper to taste.