In 1-cup microwavable measuring cup, stir together soy sauce, brown sugar, oil, lime juice, fish sauce, gingerroot and pepper flakes.
In large nonmetal dish or resealable food-storage plastic bag, place beef and 3 tablespoons of the soy sauce mixture. (Cover and refrigerate remaining soy sauce mixture for dressing). Turn to coat. Cover dish or seal bag; refrigerate at least 20 minutes or up to 4 hours to marinate.
Heat gas or charcoal grill. Remove beef from marinade; discard marinade. Place beef on grill over medium heat. Cover grill; cook 10 to 15 minutes, turning halfway through grilling, until desired doneness. Let stand 5 minutes; cut into thin strips. Cut strips into 1- to 1 1/2-inch lengths.
Meanwhile, in 2-quart saucepan, heat 6 cups water to boiling. Add rice stick noodles; cook 2 to 3 minutes or just until tender (do not overcook). Rinse in cold water until cool; drain. Cut noodles with kitchen scissors into 3- to 5-inch lengths.
Using wire whisk, mix peanut butter into remaining soy sauce mixture to make dressing. If necessary, microwave mixture uncovered on High 15 to 20 seconds to blend in peanut butter.
In large bowl, place noodles, beef, carrots, bell pepper and onions. Toss with dressing until noodles are evenly coated. Sprinkle with peanuts. Serve immediately.