Step 1Heat the oven to 350 degrees. Put the polenta in a 2-quart gratin dish and stir in the water and 1 teaspoon salt. Bake for 45 minutes. Stir in 2 tablespoons butter and return the polenta to the oven for 15 more minutes. Taste and add more salt if necessary.
Step 2While the polenta is baking, heat the olive oil over medium heat in a large skillet. Add the diced pancetta and cook until it is browned, about 10 minutes.
Step 3Pour off all but about 1 tablespoon of the fat and add the onion, carrot and celery, and cook until the vegetables have softened, about 7 minutes. Add the garlic and cook until fragrant, about 3 minutes. Add the chopped tomatoes, season with one-half teaspoon salt and freshly ground black pepper, and cook until the liquid has all but evaporated and the tomatoes have thickened into a sauce, about 15 minutes. Season to taste with salt and pepper, and remove from the heat.
Step 4When the polenta is fully cooked, spoon the pancetta and tomato sauce over the top. Scatter the Parmigiano-Reggiano over the top and return to the oven to bake until the cheese is melted, about 10 minutes.