Toast sesame seeds in medium skillet over medium heat until golden and fragrant. Watch carefully and stir frequently, being careful not to burn. Reserve 1 tablespoon of toasted sesame seeds and set aside.
In blender or food processor, purée remaining 3 tablespoons sesame seeds, peanut butter, garlic, ginger, soy sauce, vinegar, hot sauce, and sugar until smooth, about 30 - 60 seconds. With machine running, add hot water 1 tablespoon at a time until sauce has the consistency of heavy cream (up to 5 tablespoons). Set aside.
Bring large pot of salted water to boil and cook spaghetti until al dente, according to package instructions. Drain and rinse with cold water until cool to touch. In large bowl, toss cooled noodles with sesame oil.
Add scallions, carrots, red bell pepper, cucumbers, bean sprouts, and sesame-peanut sauce; toss to combine. Divide among bowls or plates and top with a sprinkling of reserved sesame seeds and cilantro, and serve.