Dice the 4 Roma tomatoes into 1/2-inch pieces, removing seed pockets. Combine in a bowl with 2 cloves minced garlic, 2 tbsp olive oil, 1 tbsp balsamic vinegar, 1/4 cup sliced basil, 1/2 tsp kosher salt, and 1/4 tsp black pepper. Rest for 10 minutes.

Preheat the broiler to high with a rack 6 inches from the heat. Arrange the baguette slices on a baking sheet, brush with the remaining 1 tbsp olive oil, and top with 1/3 cup Parmesan. Broil for 3 to 4 minutes until the edges are golden and the cheese is lightly browned. Rub the remaining 1 garlic clove over each hot slice.

Drain any pooled liquid from the tomato mixture, spoon it generously over the warm bread, garnish with extra basil leaves, and serve on a platter immediately.