How to Make It
Lightly oil a 9-by-5-inch glass loaf pan. In a large saucepan, bring the water to a boil. Add a large pinch of salt, then slowly add the fine and coarse cornmeal by handfuls, whisking constantly. Cook the polenta over low heat, whisking vigorously and often, until thickened and no longer gritty, about 45 minutes.
Meanwhile, in a small saucepan of boiling salted water, cook the corn until tender, about 3 minutes. Drain.
Stir the corn into the polenta, followed by 2 tablespoons of the butter and all of the Parmesan. Season with salt and pepper. Scrape the polenta into the prepared loaf pan and smooth the surface. Cover with plastic wrap and let cool to room temperature, then refrigerate overnight.
Cut the polenta into 8 thick slices. In each of 2 large, nonstick skillets, melt 2 tablespoons of the remaining butter in 2 tablespoons of the olive oil. Add 4 polenta slices to each skillet and cook over moderate heat until browned on the bottom, about 5 minutes. Using a spatula, scrape the slices from the bottom of the skillets and flip them. Cook until browned on the second side, about 5 minutes longer. Serve the fried polenta at once.