Use a sharp knife to cut the kernels off the cobs, reserve the kernels. Place the cobs in a large pot and add 6 cups (1.42 L) of the water. Cover the pot and bring to a simmer. Simmer for 20 minutes.
Meanwhile, prepare the vegetables. Dice the onion, celery, and carrot. Peel and cut the potato into cubes. Mince the garlic.
In a second pot, heat the oil over medium heat and add the onion and celery. Fry until soft - about 2 minutes, then add the garlic and fry until fragrant - 30 seconds.
Add the carrot, potato and remaining 1 cup (240 ml) of water. Cover the pot and bring to a simmer. Gently simmer/steam, stirring from time to time, until the potatoes are nearly cooked through - about 15 minutes. Add more water if the pot gets dry.
For the last 5 minutes, add 2 cups (280 g) of the corn kernels and continue cooking until the corn is tender.
Back to the first pot. After 20 minutes of simmering the cobs, remove the cobs from the water and add the remaining 4 cups (560 g) of corn kernels. Cover and bring to a simmer. Simmer for 5 - 10 minutes or until the corn is tender. (The cooking time will depend on how fresh your corn is. The fresher, the shorter the cooking time. Not-so-fresh supermarket corn may need up to 15 minutes).
When the corn is cooked, transfer the corn and its cooking water to a blender (or use an immersion blender) and, with the lid slightly ajar to allow steam to escape, blend well until creamy.
Place a fine mesh strainer over a large bowl and strain the contents of the blender. Use a spoon to smush the corn pulp to get out as much liquid as possible. You should just have some fibrous pulp left in the strainer and a bowl full of creamy corn broth.
Transfer the corn broth back to the pot and use a slotted spoon to transfer the cooked vegetables into the pot (without the cooking water). Add salt. If the soup has cooled down, gently warm it over medium-low heat until hot.