Sprinkle chicken with salt. Heat oil in a large nonstick skillet over medium-high heat. Add chicken. Sauté 3 minutes; turn chicken over. Add ginger, jalapeño, and garlic; cook 2 minutes, stirring often. Add peas, 3/4 cup broth, carrot, and soy sauce; bring to a boil. Cover, reduce heat, and simmer 5 minutes or until chicken is done.
Remove chicken and vegetables from pan with a slotted spoon. Combine cornstarch and 1 tablespoon broth, and add to pan. Bring to a boil; cook 1 minute, stirring constantly.
Place 1/2 cup noodles on each of 4 serving plates; top with 1/2 cup vegetables, one breast half, and sauce. Sprinkle each serving with 1 tablespoon cilantro and 1 tablespoon peanuts.