Heat the coconut oil in a large pot over medium heat. Add the diced onion and cook for 3 minutes until it starts to soften.
Stir in the minced garlic and grated ginger. Cook for 1 minute until fragrant.
Add the Thai red curry paste and stir for 30 seconds to toast it lightly.
Add the sliced red bell pepper and carrots. Cook for 2 minutes, stirring to coat the vegetables with the curry paste.
Pour in the vegetable broth and coconut milk. Bring the mixture to a gentle simmer.
Add the broccoli florets and cook for 5 minutes until they turn bright green and tender.
Stir in the fresh spinach and cook for 1 minute until it wilts.
Remove the pot from the heat. Stir in the lime juice and season with salt and black pepper to taste.
Ladle the soup into bowls and top with fresh cilantro and lime wedges before serving.