Cook the spaghetti in a large pot of boiling water according to the package directions. Pour into a colander, drain and rinse under cold running water, separating the strands while rinsing. Drain well, place in a large bowl and toss with 2 tablespoons of sesame oil. Stir in the remaining ingredients.
To make the dressing, whisk all of the dressing ingredients in a small bowl. Pour over the pasta salad and toss well. Cover and refrigerate for several hours to blend the flavors. Bring to room temperature before serving.