Remove kernels from 4 corn cobs and set aside. Break corn cobs in half. I find this easiest to do with my hands.
Make the corn stock. Heat oil in a medium pot over medium heat. Add onion and garlic and cook for 5-8 minutes or until softened. Add chile to onion mixture and and cook 30 seconds. Add corn cobs and 2 cups of water, snuggling corn cobs under water as much as possible. Bring to boiling, then reduce heat to simmer. Allow to cook for 30 minutes.
Remove corn cobs from stock and discard or compost. Reserve 1 cup corn kernels and set aside. Add remaining corn kernels and salt to pot and cook for 5 minutes over medium heat. Allow mixture to cool briefly and then add to blender. Add lime juice coconut milk to blender and blend mixture until mostly smooth. Season to taste with salt and pepper.
Meanwhile cook remaining corn kernels in now empty pot with a splash of water until just cooked, about 3-5 minutes. Sprinkle with sea salt.
Ladle soup into bowls and spoon reserved cooked corn kernels over top. Drizzle with basil oil, if desired. Enjoy!
To make the basil oil: Blanch basil oil for 10-20 seconds in boiling water. Cool immediately in ice bath. Drain and pat dry. Add to blender or food processor and add extra-virgin olive oil. Blitz until desired consistency is reached. Add a pinch or two of salt to taste. Can be stored in the refrigerator for up to 5 days. *You can skip the blanching step, knowing that the basil oil will not be quite as bright green due to oxidation. The flavor, however, will not be affected.