Butter a 10-by-14-inch baking dish. In a large skillet, melt 1 tablespoon of the butter in the olive oil. Add the mushrooms, season lightly with salt and pepper and cook over moderately high heat until the mushrooms start to exude their liquid, about 3 minutes. Reduce the heat to moderate and continue to cook, stirring occasionally, until the liquid has evaporated and the mushrooms are browned, about 20 minutes. Season with salt and pepper. Transfer half of the mushrooms to the prepared baking dish and the other half to a medium bowl. Cover the mushrooms in the bowl with plastic wrap and refrigerate.
In a medium saucepan, combine the milk and garlic with the remaining 3 tablespoons of butter and 2 teaspoons of salt and bring to a boil. Slowly whisk in the cornmeal over moderate heat. Reduce the heat to moderately low and cook, stirring often with a wooden spoon, until thickened, about 15 minutes. Season with salt and pepper. Pour the polenta over the mushrooms in the baking dish and smooth the surface. Place a piece of plastic wrap directly on the polenta and let cool to room temperature. Refrigerate overnight.
Preheat the oven to 350°. Bring the polenta to room temperature. Top the polenta with the sliced Robiola and bake in the upper third of the oven for about 45 minutes, or until the cheese is melted and golden brown and the polenta is hot throughout. Let the polenta rest for about 10 minutes.
Meanwhile, in a medium skillet, reheat the reserved mushrooms over moderately high heat until sizzling. Spoon the mushrooms on top of the polenta and serve.
The recipe can be prepared through Step 2; refrigerate overnight. Bring to room temperature before baking.