Heat 1 Tbsp. sesame oil in a large skillet over medium-high. Add reserved white and pale green parts of scallions and remaining three-quarters of tomatoes and cook, stirring occasionally, until softened and any liquid from tomatoes has evaporated, about 4 minutes. Mix in garlic and ginger; cook, stirring constantly, until fragrant, about 30 seconds. Add rice and stir to separate grains. Cook just to heat rice through, about 3 minutes.