In a large skillet, heat oil over medium heat until it shimmers. Add onion, celery and carrot and sweat 5-10 minutes until onion is translucent and carrot is just tender. Add garlic and saute 1 minute. Add tomatoes, crushing each one in your fist as you add it, along with their juices. Add parsley and oregano. Bring to a simmer and cook gently, uncovered, 15 minutes or until sauce reduces to about 3 cups. Add fresh basil and season with salt and pepper.
In a large saucepan, bring water and salt to a full rolling boil. Slowly drizzle in the polenta, whisking constantly. Once it's all added, reduce heat to low and simmer, stirring often, until thick, about 10 minutes.
Brush an 8x8x2 baking dish with olive oil. Spread 1/3 of the sauce over the bottom. Pour half the polenta over the sauce, and spread evenly. Sprinkle with half the cheese. Pour half the remaining sauce (another 1/3) over the cheese. Spread the remaining polenta over the sauce, then the remaining cheese, then the remaining sauce. Let stand at room temperature, loosely covered, 2 hours.
Preheat oven to 350°F Bake 25-30 minutes until bubbly around the edges and heated through to the middle (test by slipping a knife into the center for 20 seconds, then CAREFULLY touching the tip to your lower lip). Let cool 10 minutes before serving.