Preheat your grill to medium heat. Combine tomatoes, basil, vinegar, 1 teaspoon olive oil, and 1/8 teaspoon salt in a medium bowl and set aside.
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2.
Using a sharp knife, cut polenta into 16 even rounds. The easiest way to do this is to cut the log of polenta evenly in half, then cut each half in half again, so you have four quarters.
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3.
Lay polenta out on a baking sheet or large tray and brush lightly with 1/2 teaspoon of olive oil. Sprinkle 1/8 teaspoon salt and 1/16 teaspoon black pepper lightly across the rounds.
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Tip
Grills vary widely in temperature settings, so the settings and times you use may need to be adjusted according to your specific grill.
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