Preheat the oven to 430°F (220°C). Brush the flatbread with olive oil and place it on a sheet pan, a pizza tray, or a pizza stone (for extra crispiness). Bake it in the oven for 3 minutes.
Remove the flatbread from the oven and spread half the pesto on it evenly. Add the sliced (low-moisture) mozzarella and the halved baby tomatoes (or quartered if large ones). Season lightly with a pinch of salt. Return to the oven until the mozzarella has melted and has a few golden-brown spots, about 10 minutes (more or less depending on your oven).
Top with fresh arugula and drizzle the remaining pesto over it. Serve immediately while hot.