Toast the crostini: Preheat the oven to 375°F. Arrange the baguette slices on a baking sheet and brush lightly with olive oil. Bake for 8–10 minutes, flipping halfway, until golden and crisp. While still warm, rub one side of each slice with the cut garlic clove.
Marinate the tomatoes: Using a microplane or fine grater, grate the remaining garlic directly into a bowl with the chopped tomatoes. Add olive oil, balsamic vinegar, salt, pepper, and basil. Stir to combine and let sit for 10–15 minutes while the crostini cool.
Assemble and serve: Spoon the marinated tomatoes over the crostini just before serving. Finish with flaky sea salt or Parmesan if desired.
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