To make the vinaigrette
Pour the vinegar into a small bowl and whisk in 5 tablespoons of the extra virgin olive oil. Season to taste with salt and pepper. Set aside.
1. Toss carrots with 3 tablespoons of the olive oil, the thyme, and salt and pepper to taste.
2. Heat a large cast-iron skillet over high heat. Working in batches if necessary, add the 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 a spatula and cook on the other side for 2 to 3 minutes more, adjusting the heat as necessary, until they are crunchy on the outside and tender within. Transfer to a tray.
4. Combine the parsley and arugula on a large serving platter and toss lightly with half the vinaigrette. Place the carrots on top.
5. Toss the garlic chips over the salad and drizzle with the remaining vinaigrette.