To make polenta: Bring lightly salted water to a boil in a large saucepan. Gradually whisk in the cornmeal. Reduce the heat to low and cook until the mixture thickens and the cornmeal is tender, stirring often, about 15 minutes. Turn off heat. Add the butter and parmesan cheese. Stir until incorporated. Pour onto a greased springform pan. Set aside to cool. Once cool place in the refrigerator for 2 hours to set.
Place vegetables in a medium bowl and toss with olive oil, salt, and pepper.
Preheat a grill to medium heat.
Place vegetables on the grill and cook, about 2 minutes per side. Cut polenta into equal shape and lightly oil both sides. Place on the grill and sear, about 3 minutes per side. Serve with your favorite tomato sauce.