Yes, polenta is traditionally made through tireless stirring on the stovetop. But it also can be produced in the oven, without almost any stirring. This baked polenta with roasted marinated vegetables makes for a light main course. Serve with a green salad.
Heat the oven to 450°F. In a large bowl, toss the vegetables with 2 Tbs. of the oil, 1½ tsp. salt, and ½ tsp. black pepper. Transfer to a large rimmed baking sheet lined with parchment and roast, tossing occasionally, until the vegetables are browned and tender, about 15 minutes. Let the vegetables cool; reduce the oven temperature to 350°F.
Lightly grease an 8x8-inch baking dish with oil and add the water, polenta, Parmigiano, 2 Tbs. olive oil, and ¾ tsp. salt. Stir well and then transfer to the oven. Bake until the polenta begins to set, about 30 minutes. Give a good stir and continue baking another 15 minutes or so to let the polenta absorb all of the liquid.
Coarsely chop the vegetables. Once they are cool enough to handle, place them in a large bowl and toss with the remaining 2 Tbs. oil, the vinegar, and thyme.
Let the polenta rest for a couple of minutes, then spoon onto plates and serve, topped with the vegetables.