Position a rack about 6-inches from the broiler and preheat to high. Cut the polenta into 8 squares and transfer to a sheet pan. Pat dry with a paper towel and lightly brush with olive oil. Broil until tops are browned, about 8 minutes. Remove pan from oven.
Meanwhile, heat the olive oil in a large skillet over high heat. Add the garlic and pepper flakes, stir until fragrant, about 30 seconds. Put the spinach in the pan and season with salt, cook, stirring occasionally, until wilted, about 3 minutes. Reserve pan.
Divide the wilted spinach among each polenta square. Divide slices of the meat on top of the spinach and top each square with the cheese. Place under the broiler until cheese melts and just begins to brown, another 4 minutes.
Heat the sauce in the skillet used for the spinach. Ladle some sauce onto each of 4 plates. Place 2 polenta cakes in the middle of each plate and serve.
Put the broth and milk in a medium saucepan and bring to a boil. Slowly whisk in the polenta, reduce the heat to low, and cook, whisking occasionally, until the polenta is thick and creamy, about 15 minutes.
Pull the saucepan from the heat and whisk in the cheese, butter, salt, and pepper. Pour into a baking dish. Cover with plastic wrap and refrigerate until set, about 2 hours.
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