Bring a large pot of cold water to a boil over high heat. When the pasta water boils, salt it generously, add the spaghetti or noodles, and cook, stirring occasionally, until al dente. Drain and rinse under cold running water. Put the spaghetti in a large bowl and toss with the sesame oil.
To make the Peanut Sauce: In a blender drop in the garlic and ginger while the motor is running. When the chopping is complete, stop the machine and add the peanut butter, soy sauce, brown sugar, vinegar, and red pepper. Process until smooth, then--with the blender running--slowly pour in the water.
To serve, toss the spaghetti with the Peanut Sauce, then top with the cucumber, chicken, scallions, and peanuts.
Toasted sesame oil delivers richness and intensity to our sesame sauce with just a drizzle. Maintain its punch by storing it in your refrigerator.