Bring a large pot of water to a boil and turn off the heat. Add the rice noodles and let them soften, about 2 to 3 minutes. Drain. (Reserve 1 cup cooked noodles for Online Round 2 Recipe Summer Rolls.)
In a wok or a large skillet over high heat, add 1 tablespoon oil. When it is hot, add the eggs and cook until they are firm. Remove them from the pan and let them cool a bit. Roughly chop them and set aside.
In a small bowl, whisk together the brown sugar, soy sauce, fish sauce, chile sauce, lime juice, garlic, and broth. Set side.
Add the remaining 1 tablespoon oil to the pan along with the carrots, scallions, and bean sprouts and stir fry 1 minute. Add the reserved eggs and sauce, stirring to coat everything completely. Cook for another minute. Serve garnished with peanuts and cilantro.