Make the polenta and get the otehr ingredients ready - once it's cooked you have to be fairly quick before it sets.
Cheese - parmigiano, and another cheese - in val d'aosta they would use fontina (the real one, the stinky one) or you could use grated practically anything. I use gruyere, but it could be mozzarella (too tasteless for me but melts nicely) or could be just parmigiano.
butter a baking dish, pour or spoon some polenta on the bottom, sprinkle with cheese(s) and butter. More polenta, more cheese and butter, more polenta...you get the idea.
Top the last (uncheesed) polenta layer with butter, and bake till the butter sort of bubbles up, the top browns a little.
Otherwise you can do it with a tomato sauce and whatever you like, say, sausages (brown the sausages and then cook them in the sauce. Cut them up to add to the polenta dish. Cheese,. butter. make layers first sauce, then polenta, then cheese and butter, then more sauce, etc.
My mother in law used the fine polenta, not bramato but fiore. It's like flour but still yellow. She would pour it into soup dishes and serve with tomato sauce (no meat) and parmigiano. It makes a creamier polenta.
My impression is that the further south you go the softer the polenta is. In the far north, near austria, they make it cook so long it separates from the sides of the pot and they turn this large ball onto a board and cut it with a string. In val d'aosta (near french border) it was less hard, as in Tuscany where my parents came from (they would make it impaticciata), and in Latium, my inlaws ate it very soft, with a spoon from a soup bowl.