Add the carrots, shallot, celery, sea salt, and pepper. Stir-fry until the vegetables are tender, about 5-7 minutes. Stir in the cooked black rice and balsamic vinegar. Mix well to combine.
Transfer the rice mixture to a 9-by-13-inch baking dish. Cover loosely with aluminum foil. Bake until tender, about 30 minutes. Remove from the oven, top with the scallions, and serve.