Preheat a grill pan over medium heat. While it heats up, thinly slice the tomatoes and finely chop them along with half of the fresh basil leaves.
Brush both sides of each bread slice lightly with olive oil to prevent sticking during cooking. Toast or grill your sliced bread until it's golden brown on each side, which should take about 1-2 minutes per side depending on the thickness of your slices.
Toss together tomato mixture and remaining basil in a bowl. Crumble mozzarella over top. Right before serving or plating, add balsamic vinegar reduction as desired for extra flavor, or drizzle with olive oil if you prefer.
Place each slice of bread on the grill pan and immediately spoon tomato mixture onto it. Add a dollop of mozzarella. Grill briefly until cheese is slightly melted, then remove from heat.