Cook noodles in boiling water 5 minutes or until done. Drain and rinse with cold water; drain well. Set aside.
Heat oil in a large Dutch oven over medium-high heat. Add onion; sauté 4 minutes or until tender. Stir in 2 cups of water and the next 9 ingredients (water through bamboo shoots). Bring to a boil; reduce heat, and simmer 30 minutes.
Combine cornstarch and 2 tablespoons water in a small bowl. Stir cornstarch mixture into soup. Bring to a boil; cook 1 minute, stirring constantly. Stir in chicken; cook 3 minutes or until chicken is done. Place 1/3 cup noodles and 1 1/2 cups soup into each of 6 large soup bowls. Sprinkle 1 teaspoon cilantro over each serving.