Toast sesame seeds in a skillet over medium heat, stirring frequently until golden and fragrant
Reserve 1 Tablespoon sesame seeds for garnish
In a blender or food processor, puree remaining 3 Tablespoons sesame seeds, peanut butter, garlic, ginger, soy sauce vinegar, hot sauce and brown sugar until smooth. Add hot water 1 Tablespoon at a time until sauce has the consistency of heavy cream.
Bring 6 quarts of water to a boil, salt water and cook noodles, 4 minutes for fresh and 10 for dried.
Drain and rinse noodles with tap water until cool to touch.
In a large bowl toss noodles with 2 Tablespoons sesame oil until evenly coated.
Add shredded chicken, green onions, carrots, cucumbers, and sauce and toss to combine.
Garnish with remaining sesame seeds