
Preheat oven to 450°F.
Toss beets, oil, dill, salt and pepper together in a large bowl. Arrange the beets in a single layer in a 9-by-13-inch metal baking pan. (Do not use a glass dish, which could shatter.) Roast, turning once, until tender and browned on both sides, about 35 minutes.
Turn the beets again. Stir broth and vinegar together in a measuring cup; carefully pour into the pan. Continue roasting until the liquid is mostly absorbed and the beets are very soft, about 20 minutes more. Sprinkle with goat cheese and garnish with more dill, if desired.