Heat the oven to 400F. Brush the baguette slices with oil on both sides and bake 6 to 8 minutes until dry and lightly golden. Let them cool completely.
Seed the tomatoes before dicing. Scooping out the watery seed pockets is the single step that keeps bruschetta from flooding the bread.
Toss the diced tomatoes with the minced garlic, balsamic, 3 tablespoons oil, salt, and pepper. Let it sit at room temperature at least 20 minutes.
Rub the cut side of the whole garlic clove across each cooled toast. It leaves just enough garlic without any raw bite.
Stir the basil into the tomatoes right before serving, then spoon onto the toasts. Add shaved Parmesan if you like.