Put a large pot of water over high heat to boil. In a food processor or blender, combine all the ingredients for the dressing. Blend until smooth. (Taste dressing, adjusting acid, saltiness or sweetness as desired.) If dressing is too thick (it should be a thin, pourable texture), add 1-2 tablespoons of water and blend again.
Salt the boiling water with a few, large pinches of salt. Add the broccoli and cook for 2-3 minutes until crisp-tender. Remove broccoli with a slotted spoon or spider into a bowl. Place in colander and rinse under cold water to stop the cooking. Leave to drain in the colander.
In the same pot of boiling water, cook noodles according to package instructions. Drain. Combine noodles, broccoli, carrots, bell peppers, scallions and sesame seeds in a large mixing bowl. Dress with 3/4 of the dressing and toss well to combine. If noodles need more dressing, add more. Otherwise, reserve extra dressing to re-dress leftovers or another use.
Place noodle salad on a serving platter or bowl. Garnish with reserved scallions and sesame seeds, chopped peanuts or cashews, as desired.