Preheat the oven to 450 degrees F (230 degrees C). Grease an 8x8-inch baking dish.

Heat water, milk, and 1 tablespoon butter in a saucepan over medium-high heat; bring to a boil. Stir in polenta with a wooden spoon until thickened, about 5 minutes. Off heat, stir in 1 cup Parmesan cheese and 1/2 chopped basil; season with salt and pepper. Transfer to the prepared baking dish; arrange 1 tablespoon chilled pieces butter over top.

Bake in the preheated oven until bubbly and beginning to brown, 15 to 20 minutes. Remove from oven.

Decoratively arrange tomato slices over top of polenta; sprinkle remaining 1/2 chopped basil over tomatoes, then sprinkle with remaining 1/2 cup Parmesan cheese.

Return to oven; bake until tomatoes warm and Parmesan bubbly, 5 to 10 minutes.