Toss the tomatoes with the balsamic vinegar, 1/4 teaspoon salt and a few grinds of pepper in a medium bowl. Set aside until juicy, about 5 minutes. Toss the arugula with the olive oil, a pinch of salt and a few grinds of pepper in a large bowl.
Spread the arugula on a platter. Spoon the tomatoes and their juices on top, then drizzle with more olive oil and vinegar. Top with parmesan.