Set aside 1/2 cup each of the beets and carrots for the dressing. Place the remaining beets and carrots in a 9×13 inch baking dish, drizzle with 1 tablespoon of olive oil, sprinkle with the sea salt, and toss to coat. Cover the dish with aluminum foil.
Bake the vegetables in the preheated oven for 15 minutes.
Meanwhile, place the reserved beets and carrots into a blender. Add the orange juice, lemon juice, vinegar, honey, ginger, soy sauce, and remaining 1 tablespoon olive oil. Blend until smooth. After the vegetables have roasted for 15 minutes, stir in the citrus sauce, then recover, and continue cooking until the vegetables are tender, about 45 minutes more.