Sauté: In a large pot, heat the olive oil over medium heat. Add the diced onion and a pinch of salt and saute 2-3 minutes until is starts to soften. Add the celery, garlic, and ginger, sautéing until the onion is translucent and everything is aromatic, about 5 more minutes. Don let anything brown; reduce the heat if needed.
Add Spinach: Stir in the fresh spinach, cooking until it wilts down but remains vibrant green, about 2-4 minutes. Add it in batches if needed (it will cook down!).
Blend: Carefully transfer the mixture to a blender, and add the water (or stock), jalapeno, lime juice, and coconut milk and puree until smooth, about 90 seconds. Scrape down the sides if needed. (You can alternatively add all remaining ingredients to the pot and use an immersion blender, but it might not be as smooth.)
Final Touches: The soup should be hot right after blending, so serve immediately, or return the soup to the pot and heat through on low heat for 5-10 minutes. Garnish with freshly chopped mint (we highly recommend this for the flavor!) and a swirl of coconut milk, if desired.