Prepare the rice and ginger scallion sauce.

In a mixing bowl, beat the eggs well with salt to taste (the eggs are raw at this point), sesame oil, and rice wine. In a small bowl, stir together the cornstarch and 4 tablespoons of water until well combined, then stir in the sugar and ketchup.

If using fresh tomatoes, cut them into ½-inch wide wedges.

Heat a large nonstick skillet over high heat with 3 tablespoons of oil. When the oil is lightly smoking, add most of the scallions, saving some to garnish. Cook, stirring, until very aromatic, about 20 seconds. Add the eggs and cook, stirring well with a spatula or chopsticks, until just-set but still runny, about 45 seconds. Pour the egg back into the mixing bowl and wipe out the pan.

Reheat the pan over high heat with the remaining tablespoon of oil. When hot, add the ginger and cook until aromatic, about 15 seconds. Add the tomatoes and salt to taste; cook, stirring occasionally, until the flesh has softened but still has some shape and the juices have begun to form a sauce, 4 minutes. (If using canned tomatoes, add the juice as well and cook for about 4 minutes to reduce it to a sauce-like consistency.)

Reduce the heat to medium. Give the cornstarch-ketchup mixture a stir in its bowl, then quickly stir it into the pan. Cook, stirring, until the mixture returns to a boil and thickens.

Taste and adjust seasoning with salt, sugar, or more ketchup — you want a savory, tart-sweet sauce. Stir the eggs in the bowl to cut up the curds a bit, then return them to the pan. Cook, stirring, for a few seconds to finish cooking the eggs and to combine.

Top with the reserved scallions and serve with steamed rice.