Shred the carrots and cut the bell pepper into thin strips. Chop the green onions, mince the garlic, and pluck the cilantro. Rinse and check the bean sprouts for any spoiled individuals. Crack the eggs into a measuring cup and beat them lightly. Slice the lime into wedges.

Prepare noodles according to package directions. Drain; rinse well and drain again. In a small bowl, mix together brown sugar, soy sauce, vinegar, fish sauce, and lime juice.

In a large nonstick skillet, heat oil over medium-high heat; stir-fry carrots and pepper until crisp-tender, 3-4 minutes. Add green onions and garlic; cook and stir 2 minutes. Remove from pan.

Reduce heat to medium. Pour eggs into same pan; cook and stir until no liquid egg remains. Stir in carrot mixture, noodles and sauce mixture; heat through and continue to cook until the sauce is thickened. Add bean sprouts; toss to combine. Top with cilantro and, if desired, peanuts. Serve with lime wedges.