To prepare meatballs & roasted peppers: Position racks in upper and lower thirds of oven; preheat to 375°F.
Combine turkey, mushrooms, chopped onion, rosemary, ⅜ tsp. salt, and ½ tsp. pepper in a large bowl; mix well. Using your hands, shape the mixture into about 30 meatballs (1½-inch); arrange on a large baking sheet, spacing them at least 1 inch apart.
Combine sliced onion, bell peppers, oil, ¼ tsp. salt, and the remaining ½ tsp. pepper in a large bowl; toss to coat. Gently mix in tomatoes. Spread the mixture in a single layer on another large rimmed baking sheet.
Bake both the meatballs and the vegetable mixture, flipping the meatballs and stirring the vegetables after 12 minutes, until an instant-read thermometer inserted into several meatballs reads 165°F and the vegetables are tender, 22 to 25 minutes.
Meanwhile, prepare polenta: Bring water and salt to a boil in a large saucepan. Gradually add cornmeal, whisking constantly. Continue whisking until the polenta starts to thicken, 1 to 2 minutes. Reduce heat to low, partially cover, and cook, stirring occasionally, until very thick, about 20 minutes. Remove from heat.
Pour 2 cups of the polenta onto a large rimmed baking sheet (or toaster-oven tray) lined with parchment paper; spread evenly into a 6x8-inch rectangle and set aside to use for Polenta Pizza, if desired. Pour 2 cups of the remaining polenta into a small dish to reserve for Polenta Cakes with Poached Eggs & Avocado, if desired. Once cool, cover and refrigerate both dishes for your future meals (see Associated Recipes).
Add Parmesan and butter to the remaining 4 cups of polenta in the pot and stir to combine well. Serve the polenta topped with the roasted vegetable mixture and 20 of the meatballs. (Refrigerate 10 meatballs for another use, such as Quick Meatball Banh Mi Sandwich; see Associated Recipes.)
Tip: Any type of cornmeal can be used for polenta, but we like medium- or coarse-ground cornmeal for its great texture. It's usually labeled "cornmeal," but some brands are labeled "polenta." Look for it near whole-grain flours. Store it airtight in the freezer.