Eggplant and Mushroom Polenta Bake

1. 1
   Heat the oven to 350°F and arrange a rack in the middle. Place a large, well-seasoned or enameled cast iron skillet in the oven while it is heating.
2. 2
   Once the oven is heated, carefully drizzle 1 tablespoon of the oil into the hot skillet and let it heat up for 1 to 2 minutes. Add the eggplant to the skillet and arrange it in an even layer. Roast until tender and starting to brown, stirring halfway through, about 25 minutes. Using a dry kitchen towel or potholder, carefully remove the hot skillet from the oven by its handle and place it on the stovetop. (Use care when handling the hot skillet on the stovetop.) Using a spoon, transfer the eggplant to a medium bowl; set aside.
3. 3
   Add 1 tablespoon of the oil to the skillet and place over high heat until shimmering. Add the mushrooms and cook, stirring rarely, until browned, about 8 minutes. Add the wine, stir to combine, and cook until the liquid has completely evaporated. Reduce the heat to medium low and, using a spoon, transfer the mushrooms to the bowl with the eggplant.
4. 4
   Add the remaining 1 tablespoon of oil to the skillet and heat until shimmering. Add the onion, oregano, and red pepper flakes and season with salt. Cook, stirring occasionally, until the onion has softened and is just beginning to brown, about 5 minutes. Add the garlic and cook, stirring often, until fragrant, about 1 minute more.
5. 5
   Add the olives and reserved eggplant and mushrooms, along with any accumulated juices in the bowl, and stir to combine. Add the tomatoes and water, season with salt and pepper, and stir to combine. Bring the mixture to a simmer. Reduce the heat to low and cook, stirring occasionally, until slightly thickened, about 20 minutes. Meanwhile, begin making the polenta. (When the eggplant and mushroom mixture is ready, remove from the heat, taste, and season with salt and pepper as needed; keep warm until the polenta is ready.)

For the polenta and to assemble:

1. 1
   Place the measured water, milk, and salt in a large saucepan and bring to a simmer over high heat. Reduce the heat to low and, whisking constantly, slowly pour in the polenta in a thin, steady stream until all of it is incorporated and there are no lumps.
2. 2
   Cook, whisking or stirring with a spoon every few minutes, until the polenta pulls away from the sides of the pan and the grains have softened, about 20 minutes. (If the polenta starts to get too thick before it’s done, add water 1/4 cup at a time as necessary.) Stir in the Parmesan cheese and set aside. Heat the oven to broil and keep the rack in the middle.
3. 3
   Pour the polenta over the eggplant and mushroom mixture and spread it into a smooth, even layer. Evenly sprinkle the fontina over the polenta. Place the skillet in the oven and broil until the cheese is browned and bubbling, about 4 minutes. Remove from the oven to a wire rack and let sit 5 minutes before serving.