Heat the olive oil in a large pot over medium-high heat. Add the chopped onion and cook for about 5 minutes, stirring occasionally, until soft and translucent.
Stir in the grated ginger, minced garlic, and red curry paste. Cook for about 30 seconds until fragrant.
Pour in the broth, water, and lime juice. Add the rice noodles and bring the soup to a gentle boil.
Stir in the coconut milk and shredded chicken. Reduce the heat to medium-low and let the soup simmer for about 10 minutes, until the noodles are tender.
Add the basil, cilantro, and green onions. Season with salt and pepper to taste.
Serve hot with extra lime wedges on the side, if desired.