Soak noodles according to package instructions. Drain. In a small bowl, whisk together brown sugar, lime juice, and soy sauce.
In a large nonstick skillet, heat oil over medium-high. Add scallion whites and garlic and cook, stirring constantly, until fragrant, 30 seconds. Add eggs (if using) and cook, scraping skillet with a rubber spatula, until eggs are almost set, about 30 seconds. Transfer egg mixture to a plate. Add noodles and soy-sauce mixture to skillet; cook, tossing constantly, until noodles are soft and coated with sauce, about 1 minute. Add egg mixture and toss to coat, breaking eggs up gently. Serve noodles with lime wedges, topped with scallion greens, cilantro, and peanuts.
Any dried, flat rice noodles will work; find them in the Asian-foods section. Easy add-ins: Before adding the noodles, toss thinly sliced chicken breast or peeled and deveined shrimp into the pan.