Heat the stock in a large, deep saucepan.  Strip the kernels from the corn and add the cobs to the stock (break them in half if necessary to fit inside the pot). Let them simmer there while you prepare the other vegetables.

Place the butter or oil in a large, deep saucepan or casserole and turn the heat to medium.  A minute later, add the onion and cook, stirring, until it begins to soften, about 5 minutes.  Add the tomatoes, zucchini, garlic, salt, and pepper, and cook, stirring occasionally, for about 10 minutes.
Remove the corn cobs from the stock and add the stock to the vegetables.  Cook until the zucchini is tender but not mushy, about 5 minutes.  Add the vinegar.  Taste and adjust the seasoning as necessary.
Serve, garnishing with the remaining basil.