Cut the kernels off the ears of corn by starting to cut halfway down the ear and slicing to the bottom, rotating the ear as you go; don't try to cut too close to the base of the kernels. Turn the ear over and repeat to remove all the kernels. You'll need 3-1/2 to 4 cups of kernels for the soup.

Stand one cob on end in a pie plate or other shallow dish and use the back edge of the knife to scrape the cobs and extract as much "milk" and solids as you can. Set this raw corn purée aside.

Break the cobs in half and put them in a heavy 4-quart pot. Add 6 cups water and 1 tsp. salt and bring to a boil over high heat. Reduce the heat to medium low, cover, and simmer for 30 min. Discard the cobs. Pour the liquid into a bowl and set aside.

Set the pot back over medium-high heat and add the oil or butter (or both). When it's hot, add the onion and sauté until translucent, about 3 min. Add the garlic and cook for 1 min. Reduce the heat to medium, add the celery, sprinkle with salt, and stir. Cover the pot and cook, stirring occasionally, until the vegetables start to soften, 5 to 6 min.; don't let them color. (If they start to brown before softening, reduce the heat.) Add the potatoes, marjoram, black pepper (about 6 turns of the grinder), and cayenne and stir to distribute the seasonings. Add the corn stock. Bring to a boil over medium-high heat, cover, lower the heat to medium low, and simmer until the vegetables are tender enough to purée, 20 to 30 min. Add most of the corn kernels, reserving about 1 cup. Simmer gently for another 10 min.

Purée the soup in batches in a blender (be careful to fill the blender no more than one-third full and hold a towel over the lid while you turn it on). Put the puréed soup back in the pot. Taste for seasoning and add more salt or pepper if necessary. Add the reserved corn kernels and corn "milk," and simmer just long enough to take the raw edge off the corn, about 5 min. Serve hot, warm, or at room temperature, garnished with a small dollop of sour cream and the tomatoes and basil.