Spaghetti with Spicy Chicken and Peanut Sauce

Pound chicken between sheets of wax paper to 1/4-inch thick. Rub with sesame oil. Heat a large nonstick skillet over high heat. Add chicken breasts. Cook 2 to 3 minutes per side, turning once until cooked through. Remove to a plate. Cook spaghetti in a large pot of salted boiling water until al dente, about 8 minutes. Stir in broccoli and drain. Rinse with cold water until cool. Drain. Cut chicken breasts into thin diagonal strips. In a large bowl, combine pasta, all but 2 tablespoons of scallions, red bell pepper, 1/4 cup peanut sauce, and lime juice. Toss until mixed. Divide pasta among plates. Arrange chicken in center of pasta. Drizzle with remaining peanut sauce. Sprinkle with remaining scallions and chopped peanuts.