Preheat the oven to 425°. On a large rimmed baking sheet, toss the potatoes and garlic cloves with the olive oil. Spread the potatoes in an even layer, cut sides down. Season with salt and pepper and sprinkle with the chopped thyme. Bake for about 30 minutes, or until the potatoes are browned on the bottom and very crisp. Peel the garlic cloves. Transfer the potatoes and garlic to a platter, sprinkle with the parsley leaves and serve.