In a large saucepan, combine the scallion whites, carrots, broth, soy sauce, Shaoxing, ginger, sugar, and 1/4 tsp. pepper. Bring to a simmer over medium-high heat, stirring once or twice. Cover, reduce the heat to low, and simmer gently for 5 minutes. Add the tofu, cover, and continue to simmer gently until the tofu is heated through and has absorbed some of the other flavors, 10 minutes.
In a small bowl, whisk the vinegar and arrowroot until smooth and then stir the mixture into the stew, taking care not to break up the tofu. Stir gently until thickened, about 1 minute. Add more soy sauce to taste, sprinkle with the scallion greens, and serve.