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, prep them first. Heat the broiler to high.
Place the tomatoes, olive oil, and garlic in a small skillet or oven-safe dish. Season with a pinch of salt, then toss to coat. Transfer pan to the broiler and broil for 10 to 15 minutes, checking every five minutes — if the tomatoes are blistering within 5 minutes, lower the rack. Ultimately the tomatoes should be both blistered and jammy.
Remove pan from the broiler, and stir in the handful of basil.
Working over a large bowl, grate the kernels off of the cob on the coarse side of a box grater. You will have a very wet coarse pulpy mixture.
Melt the butter in a small saucepan over medium heat. Add the grated corn and season with a good pinch of salt. Simmer over low heat, stirring to prevent browning, for about 3 minutes. The mixture is ready when it just begins to thicken and set.
Spoon the polenta into a serving bowl. Top with the jammy, blistered tomatoes. Top with some grated Parmigiano Reggiano and pepper to taste if you wish.