Preheat grill to medium-high heat, about 400 ̊F-500 ̊F.
In a blender or food processor, pulse the basil leaves and lemonzest together until the basil is chopped up. While the motor is running, add the oil through the feed tube untilyou have a smooth purée (between 30 and 60 seconds). Set aside. Cut the haloumi into 1⁄2-inch-thick slices. Quarter the peaches.
Drizzle and toss the haloumi and peaches with olive oil.
Grill the peaches until grill marks appear on the flesh sides.
Grill the haloumi on each side until grill marks appear and thecheese releases. In the meantime, gently toss the arugula with some of thevinaigrette. Place on a platter. Top the dressed arugula with the grilled peaches and haloumi.
Drizzle with the balsamic vinegar, sprinkle with flaked salt, crackedpepper and a little more olive oil. Dollop a little more vinaigrette ontop of the grilled haloumi and peaches. Serve warm or at room temperature.