1. Bring a large saucepan of water to a boil over high. Remove from heat. Submerge noodles in water until tender, about 3 minutes. Drain; rinse with cold water.
2. Preheat oven to 450 degrees F with racks in upper- and lower-third positions. Toss together mushrooms, asparagus, garlic, and 2 Tbs. of the sesame oil on a large rimmed baking sheet. Toss together tofu and remaining 1 Tbs. sesame oil on a separate large rimmed baking sheet. Place mushroom mixture on upper rack and tofu on lower rack of preheated oven. Roast mushroom mixture, stirring twice, until tender, about 15 minutes. Remove from oven; set aside. Increase oven temperature to broil. Stir tofu, and move to upper rack. Broil until lightly browned, about 4 minutes.
3. While mushroom mixture and tofu cook, microwave vinegar in a microwave-safe bowl until steaming, about 1 minute. Stir in carrots; let stand until…