Combine first 8 ingredients in a jar; cover tightly, and shake. Slice chicken diagonally into 1/2-inch slices.
Set aside 2 cups spinach leaves. Stack remaining spinach leaves, and cut into thin slices; set aside.
Cook noodles according to package directions, omitting salt and fat; drain. Transfer noodles to a large bowl; add 1/3 cup broth mixture, sliced spinach, cilantro, green onions, and gingerroot; toss lightly.
Pour remaining broth mixture into a large nonstick skillet; place over medium-high heat until hot. Add chicken; saute 2 minutes. Add red pepper; saute 3 to 4 minutes or until pepper is tender.
To serve, place 1/2 cup spinach leaves on each of 4 plates. Arrange noodle and chicken mixtures over spinach; sprinkle with peanuts.