Place the peanut butter in a medium-sized bowl and mash with the back of a soup spoon to soften. Add about half the hot water, and continue to mash, very gently and slowly so as not to splash, until uniform. Add the remaining hot water, and patiently mix until smooth.
In a small food processor, blend vinegar, salt, garlic, ginger, sugar, soy sauce, sesame oil, and cayenne pepper. Stir into the bowl with peanut mixture until well combined.
Place the noodles in a large bowl, and pour the sauce over the noodles. Mix with a fork until all the noodles are coated.
Serve topped with cucumber, shredded carrot, scallions, sesame seeds, nuts and cilantro.