Beat the eggs with 1/2 tsp salt until smooth but not frothy.
Heat 1 tbsp oil in a nonstick skillet over medium-high heat. Add the eggs and cook undisturbed just until a thin film forms on the bottom but most is still runny (5-10 seconds). Immediately scrape into a bowl and wipe out the skillet.
Heat the remaining 1 tbsp oil over medium-high heat. Add scallions and stir-fry until softened (about 30 seconds). Add tomatoes and cook, stirring, until juices release and tomatoes are slightly wilted but intact (4-6 minutes). Sprinkle over the sugar and 1/4 tsp salt, add tomato sauce if using, and stir. Return the eggs and cook until just set. Serve sprinkled with the reserved scallion greens.
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