Position rack in upper third of oven; preheat to 500 degrees F.
Toss sweet potatoes, butter, oil, thyme, rosemary, paprika, 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, as it could shatter.) Roast, flipping once, until browned, 25 to 30 minutes.
Whisk broth and garlic in a measuring cup. Carefully add the broth mixture to the hot pan. Continue roasting until most of the liquid has been absorbed and the potatoes are very tender, about 15 minutes more. Serve hot.
