In a small nonstick skillet, heat oil over medium heat. Add scallions and cook until fragrant and beginning to soften, about 2 minutes. Add tomatoes and salt; cook, stirring occasionally, until tomatoes have softened and given off some of their juices, about 3 minutes. Remove the pan from the heat, cover, and keep warm.
Bring a large saucepan of water to a boil; add vinegar. Crack 1 egg into a cup. Gently slide egg into the water. Repeat with the remaining egg, using a slotted spoon to keep eggs separated from each other, if necessary. Cook at a simmer until yolks are lightly set, 3-4 minutes.
Divide tomato-scallion mixture between 2 shallow bowls. Top each with an egg. Spoon any remaining liquid from the tomato mixture over the eggs.