Mix all the ingredients for the sauce until smooth using a hand blender or food processor (it can also be whisked by hand but it's harder to mix the sauce properly).
Cut the chicken into 1-inch (2-3cm) cubes and toss with finely chopped ginger and garlic, and season it with salt and pepper. Set aside (if you have time you can leave the chicken to marinate for a couple of hours or overnight).
Prepare the vegetables: cut off the hard core of the cabbage, cut into thin slices, cut the carrots into thin matchsticks, cut the bell paprika into thin strips, cut the broccoli into very small florets.
Cook the noodles according to the package instructions, make sure they are cooked al dente - which means they should have a bite to them / be pleasantly chewy and not be overcooked. My package says to cook them for 4 minutes so I pour boiling water over them the cook them for about 3 minutes as they will cook later a little in the pan.
Cook the chicken: toss the chicken pieces with cornstarch (you should do that directly before you plan on cooking it). Heat the oil in a big frying pan over high heat. When hot add the chicken pieces in an even layer. Don't stir for the first 2 minutes, letting the chicken to brown. When the chicken is browned turn it over and cook briefly on the other side until cooked thorugh. Transfer the chicken to a plate.
Cook the vegetables. Add some more oil to the pan and add the vegetables. Don't stir at the beginning letting the vegetables brown then stir and cook for a couple of minutes until the vegetables are tender but still a little crunchy.
Add the chicken back to the pan, then the cooked noodles and the sauce. Toss everything together. Cook for a minute allowing the sauce to thicken a little. Serve sprinkled with toasted peanuts.