Cook soba noodles as directed on package, then rinse with cold water.
Meanwhile, crush garlic and grate ginger for the dressing. Mix all dressing ingredients together in a small bowl and set aside.
Peel carrots and cut them into matchstick-like strips; thinly slice cabbage and onion. Add all to a large mixing bowl, along with shelled edamame and sesame seeds; toss to combine.
Just before serving, toss noodles, sauce, and vegetables together. Serve with watermelon on the side.