How to Make It
In a medium saucepan, bring 41/2 cups of the water and 1 teaspoon of the salt to a boil. Add the cornmeal in a slow stream, whisking. Whisk in the butter. Reduce the heat and simmer, stirring frequently with a wooden spoon, until the polenta is very thick, about 20 minutes. Cover to keep warm.
Meanwhile, in a large deep frying pan, heat the oil over moderately low heat. Add the onion and cook, stirring occasionally, until translucent, about 5 minutes. Add the garlic and cook, stirring, for 1 minute. Add the tomatoes, vinegar, oregano, and jalapeño. Cook, stirring frequently, for 5 minutes.
Add all the mushrooms, the cabbage, and 1 cup of the water to the pan. Bring to a boil. Cover and reduce the heat to moderately low. Simmer, stirring occasionally, for 15 minutes. Add the remaining 1 cup water and 2 teaspoons salt and simmer, covered, until the vegetables are tender, about 10 minutes more. Stir in the cilantro and serve over the polenta.