Heat the coconut oil in a large pot over medium heat. Add the onion and cook until it softens, about 3 minutes.
Stir in the garlic and ginger, then cook for 1 minute until fragrant. Add the green curry paste and stir for another minute to release its aroma.
Pour in the vegetable broth and coconut milk. Bring the mixture to a gentle simmer.
Add the carrots and red bell pepper. Cook for 5 minutes, then add the zucchini and broccoli. Simmer for another 5 minutes until the vegetables are tender but not mushy.
Stir in the spinach and cook just until it wilts, about 1 minute. Remove the pot from heat and stir in the lime juice.
Ladle the soup into bowls and top with chopped cilantro. Serve with lime wedges on the side.