Cut the baguette in half lengthwise, place on a sheet tray and bake in the oven until lightly brown. Rub with the garlic cloves. Drizzle with 2 ounces of the olive oil and sprinkle with the Parmigiano-Reggiano. Return to oven to melt cheese.
In a medium mixing bowl, add the tomatoes, minced garlic, basil, vinegar, remaining olive oil, salt and pepper. Mix thoroughly and let sit for 5 minutes at room temperature.
Remove baguette from oven and top with the tomato mixture. Garnish with basil and Parmigiano-Reggiano.