In a large pot over medium, heat the oil until shimmering. Add the scallion whites and ginger; cook, stirring, until fragrant, about 30 seconds.
Add the potatoes, corn, broth and coconut milk. Bring to a simmer over medium-high, then reduce to medium and simmer, uncovered and stirring occasionally, until the potatoes are tender, about 15 minutes.
Off heat, stir in the fish sauce, lime juice and scallion greens. Serve with lime wedges.