Poach the chicken breasts: place the chicken breasts in a pot large enough so they’re sitting beside each other on the bottom of the pot; pour in just enough water to cover the chicken pieces and add the ginger slices; bring the water to a boil, then immediately reduce the heat to low and simmer until when you poke a thermometer into the widest part of the breast the internal temperature reaches 74°C (165°F). Remove the chicken breasts and when they’re cool enough to touch, shred the chicken pieces into strips using your hands or two forks and set aside to cool.
While the chicken is poaching, boil the noodles in a big pot of salted water according to the instructions on the packet, then drain, rinse under cool water, transfer to a cold mixing bowl, douse in a tablespoon of sesame oil, ensuring the noodles are completely coated, and refrigerate until ready to assemble.
Prepare the salad dressing: to a jar with lid, add a tablespoon of sesame oil, Chinese sesame paste, dark soy sauce, rice vinegar, minced ginger and garlic, sugar and salt, screw the lid on and shake the jar vigorously. Taste and adjust the seasoning if needed.
Assemble the salad: to the noodles, add the shredded chicken, cucumber ‘noodles’, sliced scallions, sliced red chillies, half the pan-roasted peanuts, sesame seeds and fresh coriander, and the dressing, and combine well. Refrigerate to chill if you're not ready to eat it yet.
Just before serving, transfer it to a salad bowl or serving plate, sprinkle with the other half of the pan-roasted peanuts, sesame seeds and fresh coriander, and serve immediately.