Heat the olive oil in a large pot over medium heat. Add the diced onion, minced garlic, and grated ginger. Cook for 2 minutes until the onion softens.
Stir in the Thai red curry paste and cook for 1 minute to release its aroma.
Add the sliced red bell pepper, carrots, and zucchini. Stir to coat the vegetables with the curry paste.
Pour in the vegetable broth, coconut milk, and soy sauce. Bring the mixture to a gentle simmer.
Cook for 10 to 12 minutes until the carrots are tender but still have some bite.
Stir in the fresh spinach and lime juice. Cook for 1 minute until the spinach wilts.
Ladle the soup into bowls and top with fresh cilantro. Serve with lime wedges on the side.