Preheat oven to 400 degrees F (200 degrees C).
Brush bread slices on both sides lightly with 1 tablespoon oil and place on large baking sheet. Toast bread until golden, 5 to 10 minutes, turning halfway through.
Meanwhile, toss together tomatoes, basil, Parmesan cheese, and garlic in a bowl.
Mix in balsamic vinegar, 2 teaspoons olive oil, kosher salt, and pepper.
Spoon tomato mixture onto toasted bread slices.