Cook the spaghetti in a large pot of boiling water as the package label directs. Just before draining, add the broccoli, edamame, carrots, and spinach. Drain well; set aside.
In the same pot, heat 2 tablespoons of sesame oil on medium-high. Add the onion; cook for 5 min.
Add the ginger, soy sauce, and balsamic vinegar.
Cook for 1 minute. Stir in tofu and cook for 1 minute. Add the noodle mixture; cook, tossing for 2 minutes or until heated through.