Step 1

Position rack in upper third of oven; preheat to 500 degrees F.

Step 2

Toss potatoes, butter, oil, thyme, salt and pepper in a large bowl. Arrange in a single layer in a 9-by-13-inch metal baking pan. (Don't use a glass dish, which could shatter.) Roast, flipping once, until browned, about 30 minutes.

Step 3

Whisk garlic into broth; carefully add the broth mixture to the pan. Sprinkle the tops of the potatoes with Parmesan. Continue roasting until most of the broth has been absorbed and the potatoes are very tender, about 15 minutes more. Serve hot.