Shuck the corn and cut the kernels from the ears with a sharp knife. Blanch, core, and skin the tomatoes. Then, chop coarsely in a food processor, retaining all juices (use just a few short pulses or you will make puree). Finely mince the jalapeños. Clean and slice the mushrooms. Set aside.
Heat the olive oil in a heavy soup kettle, add the onion and red pepper, and sauté over low heat until limp. Add the jalapeños, zucchini, squash, mushrooms, and cumin and sauté a few minutes, stirring the vegetables gently. Add water and chicken stock, bring to a simmer, season with salt and black pepper, and cook over low heat for about five minutes. Add the corn, vinegar, and basil and cook about two minutes longer.