Preheat oven to 450°F. Toss sliced beets, 2 tablespoons oil, ¼ teaspoon salt and ¼ teaspoon pepper in a 9-by-13-inch metal baking pan; arrange in a single layer. (Do not use a glass dish, which could shatter.) Cover with foil. Roast until tender and easily pierced with a paring knife, about 50 minutes. Carefully remove the foil.
Stir together ¾ cup broth, 3 tablespoons vinegar, 2 teaspoons honey, 1½ teaspoons rosemary and 1 teaspoon mustard in a liquid measuring cup; carefully pour into the pan. Continue roasting, uncovered, until the beets are very tender and most of the liquid has been absorbed, about 20 minutes.
Place the pan on a heat-safe work surface; immediately add butter pieces. Gently shake the pan back and forth until the butter is fully melted and emulsified. Garnish with rosemary, if desired.
