Heat the olive oil in a large pot over medium heat. Add the chopped onion and cook until it becomes translucent in about 5 minutes.
Add the minced garlic, grated ginger, and coriander seeds. Cook for another 1-2 minutes until fragrant.
Stir in the diced zucchinis and parsnips, and cook for about 5 minutes, allowing them to soften slightly.
Pour in the vegetable broth. Bring the mixture to a boil, then reduce the heat to a simmer. Cover the pot and let it simmer for about 20-25 minutes, or until the vegetables are tender.
Use an immersion blender or a regular blender to puree the soup until it's smooth and creamy. If using a regular blender, be sure to cool the soup slightly and blend it in batches.
Return the blended soup to the pot. Stir in the coconut milk for a creamy and tropical twist. Season with salt and pepper to taste
Heat the soup over low heat until it's hot and ready to serve.
Ladle the zucchini and parsnip soup into bowls, drizzle olive oil, and garnish with fresh coriander for extra flavor.