Preheat oven to 450 degrees F (230 degrees C). Grease an 8x8 inch baking dish.
Place the water, milk, and butter in a saucepan and bring to a boil over medium-high heat. Add the polenta and stir with a wooden spoon until thickened, about 5 minutes. Remove from heat and stir in 1 cup Parmesan cheese and 2 chopped basil leaves; season with salt and pepper to taste. Transfer the polenta to the prepared baking dish and arrange the remaining chilled pieces of butter over the top.
Bake the polenta in the preheated oven until bubbly and beginning to brown, 15 to 20 minutes. Remove from the oven.
Decoratively arrange the slices of tomato over the top of the polenta, spread the remaining basil leaves over the tomatoes, and sprinkle with 1/2 cup Parmesan cheese.
Return to the oven and bake until the tomatoes are warm and the Parmesan cheese is bubbly, 5 to 10 minutes.