Cook noodles according to package directions. Meanwhile, in a small bowl, combine water, soy sauce, peanut butter, brown sugar, lemon juice, garlic and pepper flakes; set aside., In a large skillet, heat 1 tablespoon oil over medium-high heat. Add chicken; stir-fry until no longer pink, 3-4 minutes. Remove from pan. , Stir-fry broccoli and carrot in remaining oil until crisp-tender, 4-6 minutes. Add soy sauce mixture; bring to a boil. Cook and stir until sauce is thickened, 1-2 minutes. Return chicken to pan; heat through. Drain noodles; toss with chicken mixture in pan. If desired, sprinkle with sesame seeds.