Heat olive oil in a large soup pot over medium heat. Add sliced carrots first and cook for a couple of minutes to soften them slightly. Then add bell peppers, onion, garlic, and ginger. Stir and cook until fragrant.
Mix in the red curry paste, coating all the vegetables evenly. Pour in the broth and add the chickpeas. Stir everything together and bring the mixture to a gentle simmer.
Pour in the coconut milk and stir to combine. Let the soup cook for another 3 minutes until the vegetables are tender but still retain some bite.
Add the rice noodles to the pot and stir until they soften, about 2–3 minutes. Season with salt and pepper to taste.
Squeeze fresh lime juice into the soup and top with chopped cilantro. Serve immediately with extra lime wedges for a bright finishing touch.