Stir together all of the ingredients for the dressing. Set aside if you want a cold (thinner) dressing.
If you want a thicker dressing, place the dressing in a small sauce pan and simmer until it is about to boil. Mix water and cornstarch together into a slurry and add to dressing. Mix until it just begins to thicken.
Transfer the dressing (warm or cold) into a large bowl.
Heat broth with ground ginger in a small nonstick skillet. Season chicken to taste with salt and pepper and add to skillet. Cover and simmer is cooked through, about 8 minutes per side. Remove from heat and allow to cool.
Clean spinach. Dice the red pepper (if using) into 1/2 inch pieces. If using the red onion, slice very thin into half moon shapes. Peel the cucumber and half lengthwise. Cut into 1/4 inch thick slices. Add all vegetables to the large bowl with dressing and toss to coat. Transfer to serving bowl or plates.
Cut chicken into bite-size pieces and toss with any dressing left in the bowl. Arrange dressed chicken over the salad.