Wash the potatoes under cold running water. Peel and cut into 2-inch chunks.
In a carbon-steel wok, heat the oil over medium heat until just smoking. Add the shallots, onion, garlic, and ginger, and stir-fry for 5 minutes, or until the onion is wilted. Add the curry and cook for 30 seconds, until aromatic. Add the coconut milk, broth, potatoes, salt, and pepper. Bring to a simmer and cook over low heat until the potatoes are tender, about 15 to 20 minutes. Add the green beans and cook for another 10 minutes, or until the beans are just done.