Soak the sotanghon noodles in warm water for about 20 minutes or until softened. Drain and set aside. Cook the egg noodles according to package instructions, then drain and set aside.
In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent.
Add the sliced carrot to the pot and cook for an additional 3-4 minutes until slightly tender.
Pour in the chicken broth and bring to a boil. Reduce heat and let it simmer for about 5 minutes.
Stir in the shredded chicken, soaked sotanghon noodles, and cooked egg noodles. Add the soy sauce, and season with salt and pepper to taste. Let it simmer for another 2-3 minutes until everything is heated through.
Add the baby spinach and green onions, stirring until the spinach wilts.
Serve hot with lime wedges on the side for squeezing over the soup.