To prepare polenta, combine first 4 ingredients in a 13 x 9-inch baking dish, stirring well. Bake at 350° for 1 hour or until liquid is absorbed. Cover polenta and keep warm.
To prepare ragout, while polenta bakes, heat oil in a large Dutch oven over medium-high heat. Add onion, and sauté 5 minutes or until tender. Add mushrooms and 1/2 teaspoon salt; cook 10 minutes or until mushrooms release moisture and begin to brown, stirring occasionally. Add wine, chiles, oregano, and garlic. Reduce heat to medium, and cook 1 minute or until liquid evaporates, stirring constantly. Stir in tomatoes, and cook over low heat 15 minutes or until the mixture thickens slightly, stirring occasionally.
Spoon ragout over polenta; sprinkle evenly with cheese. Bake at 350° for 15 minutes or until cheese begins to melt. Sprinkle with cilantro.