To make the vinaigrette
Pour vinegar into small bowl and whisk in 5 tablespoons of extra virgin olive oil. Season to taste with salt and pepper. Set aside.
The Rest
1. Toss carrots with 3 tablespoons olive oil, thyme, and salt and pepper to taste.
2. Heat large cast-iron skillet over high heat. Working in batches if necessary, add carrots in a single layer and cook, without turning, until they are charred on the bottom and almost burned, 3 to 5 minutes.
3. Turn with spatula and cook on other side for 2 to 3 minutes more, adjusting heat as necessary, until charred on outside and tender within. Transfer to tray.
4. Combine parsley and arugula on large serving platter and toss lightly with half vinaigrette. Place carrots on top.
5. Toss garlic chips over the salad and drizzle with the remaining vinaigrette.