Puree peanut butter, garlic, ginger, soy sauce, rice vinegar and brown sugar in a blender until smooth. With blender running, pour in 1/4 cup hot water and blend until smooth.
Bring a pot of salted water to a boil. Cook noodles until just tender, about 9 minutes. Drain, rinse under cold water and drain again. Transfer to a large bowl; toss with sesame oil.
Toss scallions, cucumbers, carrots and sauce in bowl with noodles. Sprinkle with cilantro and sesame seeds.