Lightly oil an 11 by 7-inch baking dish. Transfer the hot polenta to the prepared baking dish, spreading evenly to 3/4-inch thick. Refrigerate until cold and firm, about 2 hours.
Preheat the oven to 250 degrees F.
Cut the polenta into 2 by 1-inch pieces. Heat the oil in a heavy large skillet over medium-high heat. Working in batches, fry the polenta pieces until golden brown on all sides, about 3 minutes per side. Using tongs, transfer the polenta pieces to paper towels and drain. Place the polenta pieces on a baking sheet and keep warm in the oven while cooking the remaining batches.
Transfer the polenta pieces to a serving platter. Sprinkle the polenta with the Parmesan cheese and salt. Serve, passing the marinara sauce alongside.
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