Combine the potatoes and salted water in a large saucepan. Bring to a boil and cook 20 minutes. Add the beans and cook until the potatoes are tender but still firm and the beans are tender, about 7 minutes. Drain the vegetables in a colander. Remove the potatoes and set them aside to cool. Refresh the beans under cold running water and drain well. When the potatoes are cool enough to handle, peel them and cut into 1/3-inch cubes.

 In a large, deep skillet, heat the olive oil over medium heat. Add the garlic and cook until golden, about 1 minute. Add the potatoes and string beans and season them with salt and pepper. Cook the vegetables, mashing the potatoes roughly, as you stir them, until the vegetables are heated through. Season to taste with salt and pepper and serve hot.