Cut the potatoes in quarters, or eighths if they are large. Small to medium-small pieces get wonderfully crisp when they roast.
Place the potato pieces in a large mixing bowl. Drizzle the olive oil over them, then add the garlic, thyme, and Parmesan. Season with the salt and pepper. Toss the potato mixture well so that the potatoes are well coated in the oil and such.
Pour the potatoes into a baking dish and roast for 45 minutes to an hour, until the potatoes are fork-tender and have lovely crispy spots on them. Serve warm.