Bring water to a boil in a heavy-bottomed saucepan over medium-high heat.
Once boiling, add 1 1/2 teaspoons salt and pour the polenta into the water in a very slow stream from a measuring cup, while stirring in a circular motion with a wooden spoon. Make sure to scrape the bottom and corners of the pot well.
Reduce the heat to the lowest setting and cover. Vigorously stir the polenta once every 5 minutes, making sure to scrape clean the bottom and corners of the pot.
Continue cooking until the polenta has lost its raw cornmeal taste and becomes soft and smooth, about 30 minutes. Stir in the Parmesan and butter and season with salt and pepper to taste.
For the tomatoes and mozzarella:
During the final 5 minute of cooking the polenta, heat the oil, garlic, pepper flakes and sugar in a nonstick skillet over medium-high heat until fragrant and sizzling (about 1 min.).
Stir in the tomatoes and cook until they just begin to wilt, about 1 min.; season with salt and pepper to taste and set skillet off the heat.
Spoon the polenta into the individual serving bowls and top with the mozzarella.
Spoon the tomato mixture with any accumulated juices over the top of the served polenta, and sprinkle with basil before serving.