Bring a large pot of water to a boil and cook the soba noodles according to the package directions. Drain them in a colander and rinse under cold water to stop the cooking and remove excess starch.
In a large mixing bowl, whisk together the sesame oil, soy sauce, grated ginger, rice vinegar, and honey until the dressing is smooth.
Add the cooled soba noodles, julienned carrots, sliced cucumber, sliced red bell pepper, shelled edamame, and sliced green onions to the bowl with the dressing.
Toss everything gently until the noodles and vegetables are evenly coated.
Sprinkle the toasted sesame seeds over the top just before serving.