makes one half sheet pan, 13- by 18-inches
Boil water, add salt, then slowly sprinkle in the polenta while stirring with a wooden spoon. Simmer gently for 10–15 minutes, stirring frequently, until texture is soft. Remove from heat, stir in olive oil or butter, cover, and let sit 10 minutes to steam.
Preheat oven to 400°F. Lightly oil a half-sheet pan, 13- by 18-inches. Scoop polenta into the pan and spread evenly.
Top with a layer of basil leaves, sprinkle with cheese, and add halved cherry tomatoes, cut side up. Bake until fragrant, cheese is very hot and melted, and polenta is beginning to dry at the edges, about 35 minutes. Let cool a few minutes and slice into serving pieces.